sop-core-0.5.0.2: True Sums of Products

Safe Haskell | None
Language | Haskell2010

Data.SOP

Contents

- n-ary datatypes
- Combinators
  - Constructing products
  - Destructing products
  - Application
  - Lifting / mapping
  - Constructing sums
  - Destructing sums
  - Dealing with ``All` c`
  - Comparison
  - Collapsing
  - Folding and sequencing
  - Expanding sums to products
  - Transformation of index lists and coercions
  - Partial operations
- Utilities
  - Basic functors
    - Mapping functions
  - Mapping constraints
  - Other constraints
  - Singletons
    - Shape of type-level lists
  - Re-exports

Description

Main module of `sop-core`

Synopsis

- data NP (a :: k -> Type) (b :: [k]) where
  - Nil :: forall {k} (a :: k -> Type). NP a ('[] :: [k])
  - (:*) :: forall {k} (a :: k -> Type) (x :: k) (xs :: [k]). a x -> NP a xs -> NP a (x ': xs)
- data NS (a :: k -> Type) (b :: [k]) where
  - Z :: forall {k} (a :: k -> Type) (x :: k) (xs :: [k]). a x -> NS a (x ': xs)
  - S :: forall {k} (a :: k -> Type) (xs :: [k]) (x :: k). NS a xs -> NS a (x ': xs)
- newtype SOP (f :: k -> Type) (xss :: [[k]]) = SOP (NS (NP f) xss)
- unSOP :: forall {k} (f :: k -> Type) (xss :: [[k]]). SOP f xss -> NS (NP f) xss
- newtype POP (f :: k -> Type) (xss :: [[k]]) = POP (NP (NP f) xss)
- unPOP :: forall {k} (f :: k -> Type) (xss :: [[k]]). POP f xss -> NP (NP f) xss
- class HPure (h :: (k -> Type) -> l -> Type) where
  - hpure :: forall (xs :: l) f. SListIN h xs => (forall (a :: k). f a) -> h f xs
  - hcpure :: forall c (xs :: l) proxy f. AllN h c xs => proxy c -> (forall (a :: k). c a => f a) -> h f xs
- hd :: forall {k} f (x :: k) (xs :: [k]). NP f (x ': xs) -> f x
- tl :: forall {k} (f :: k -> Type) (x :: k) (xs :: [k]). NP f (x ': xs) -> NP f xs
- type Projection (f :: k -> Type) (xs :: [k]) = (K (NP f xs) :: k -> Type) -.-> f
- projections :: forall {k} (xs :: [k]) (f :: k -> Type). SListI xs => NP (Projection f xs) xs
- shiftProjection :: forall {a1} (f :: a1 -> Type) (xs :: [a1]) (a2 :: a1) (x :: a1). Projection f xs a2 -> Projection f (x ': xs) a2
- newtype ((f :: k -> Type) -.-> (g :: k -> Type)) (a :: k) = Fn {
  - apFn :: f a -> g a
  }
- fn :: forall {k} f (a :: k) f'. (f a -> f' a) -> (f -.-> f') a
- fn_2 :: forall {k} f (a :: k) f' f''. (f a -> f' a -> f'' a) -> (f -.-> (f' -.-> f'')) a
- fn_3 :: forall {k} f (a :: k) f' f'' f'''. (f a -> f' a -> f'' a -> f''' a) -> (f -.-> (f' -.-> (f'' -.-> f'''))) a
- fn_4 :: forall {k} f (a :: k) f' f'' f''' f''''. (f a -> f' a -> f'' a -> f''' a -> f'''' a) -> (f -.-> (f' -.-> (f'' -.-> (f''' -.-> f'''')))) a
- type family Prod (h :: (k -> Type) -> l -> Type) :: (k -> Type) -> l -> Type
- class (Prod (Prod h) ~ Prod h, HPure (Prod h)) => HAp (h :: (k -> Type) -> l -> Type) where
  - hap :: forall (f :: k -> Type) (g :: k -> Type) (xs :: l). Prod h (f -.-> g) xs -> h f xs -> h g xs
- hliftA :: forall {k} {l} h (xs :: l) f f'. (SListIN (Prod h) xs, HAp h) => (forall (a :: k). f a -> f' a) -> h f xs -> h f' xs
- hliftA2 :: forall {k} {l} h (xs :: l) f f' f''. (SListIN (Prod h) xs, HAp h, HAp (Prod h)) => (forall (a :: k). f a -> f' a -> f'' a) -> Prod h f xs -> h f' xs -> h f'' xs
- hliftA3 :: forall {k} {l} h (xs :: l) f f' f'' f'''. (SListIN (Prod h) xs, HAp h, HAp (Prod h)) => (forall (a :: k). f a -> f' a -> f'' a -> f''' a) -> Prod h f xs -> Prod h f' xs -> h f'' xs -> h f''' xs
- hcliftA :: forall {k} {l} h c (xs :: l) proxy f f'. (AllN (Prod h) c xs, HAp h) => proxy c -> (forall (a :: k). c a => f a -> f' a) -> h f xs -> h f' xs
- hcliftA2 :: forall {k} {l} h c (xs :: l) proxy f f' f''. (AllN (Prod h) c xs, HAp h, HAp (Prod h)) => proxy c -> (forall (a :: k). c a => f a -> f' a -> f'' a) -> Prod h f xs -> h f' xs -> h f'' xs
- hcliftA3 :: forall {k} {l} h c (xs :: l) proxy f f' f'' f'''. (AllN (Prod h) c xs, HAp h, HAp (Prod h)) => proxy c -> (forall (a :: k). c a => f a -> f' a -> f'' a -> f''' a) -> Prod h f xs -> Prod h f' xs -> h f'' xs -> h f''' xs
- hmap :: forall {k} {l} h (xs :: l) f f'. (SListIN (Prod h) xs, HAp h) => (forall (a :: k). f a -> f' a) -> h f xs -> h f' xs
- hzipWith :: forall {k} {l} h (xs :: l) f f' f''. (SListIN (Prod h) xs, HAp h, HAp (Prod h)) => (forall (a :: k). f a -> f' a -> f'' a) -> Prod h f xs -> h f' xs -> h f'' xs
- hzipWith3 :: forall {k} {l} h (xs :: l) f f' f'' f'''. (SListIN (Prod h) xs, HAp h, HAp (Prod h)) => (forall (a :: k). f a -> f' a -> f'' a -> f''' a) -> Prod h f xs -> Prod h f' xs -> h f'' xs -> h f''' xs
- hcmap :: forall {k} {l} h c (xs :: l) proxy f f'. (AllN (Prod h) c xs, HAp h) => proxy c -> (forall (a :: k). c a => f a -> f' a) -> h f xs -> h f' xs
- hczipWith :: forall {k} {l} h c (xs :: l) proxy f f' f''. (AllN (Prod h) c xs, HAp h, HAp (Prod h)) => proxy c -> (forall (a :: k). c a => f a -> f' a -> f'' a) -> Prod h f xs -> h f' xs -> h f'' xs
- hczipWith3 :: forall {k} {l} h c (xs :: l) proxy f f' f'' f'''. (AllN (Prod h) c xs, HAp h, HAp (Prod h)) => proxy c -> (forall (a :: k). c a => f a -> f' a -> f'' a -> f''' a) -> Prod h f xs -> Prod h f' xs -> h f'' xs -> h f''' xs
- type Injection (f :: k -> Type) (xs :: [k]) = f -.-> (K (NS f xs) :: k -> Type)
- injections :: forall {k} (xs :: [k]) (f :: k -> Type). SListI xs => NP (Injection f xs) xs
- shift :: forall {a1} (f :: a1 -> Type) (xs :: [a1]) (a2 :: a1) (x :: a1). Injection f xs a2 -> Injection f (x ': xs) a2
- shiftInjection :: forall {a1} (f :: a1 -> Type) (xs :: [a1]) (a2 :: a1) (x :: a1). Injection f xs a2 -> Injection f (x ': xs) a2
- type family UnProd (h :: (k -> Type) -> l -> Type) :: (k -> Type) -> l -> Type
- class UnProd (Prod h) ~ h => HApInjs (h :: (k -> Type) -> l -> Type) where
  - hapInjs :: forall (xs :: l) (f :: k -> Type). SListIN h xs => Prod h f xs -> [h f xs]
- apInjs_NP :: forall {k} (xs :: [k]) (f :: k -> Type). SListI xs => NP f xs -> [NS f xs]
- apInjs_POP :: forall {k} (xss :: [[k]]) (f :: k -> Type). SListI xss => POP f xss -> [SOP f xss]
- unZ :: forall {k} f (x :: k). NS f '[x] -> f x
- class HIndex (h :: (k -> Type) -> l -> Type) where
  - hindex :: forall (f :: k -> Type) (xs :: l). h f xs -> Int
- hcliftA' :: forall {k} (c :: k -> Constraint) (xss :: [[k]]) h proxy f f'. (All2 c xss, Prod h ~ (NP :: ([k] -> Type) -> [[k]] -> Type), HAp h) => proxy c -> (forall (xs :: [k]). All c xs => f xs -> f' xs) -> h f xss -> h f' xss
- hcliftA2' :: forall {k} (c :: k -> Constraint) (xss :: [[k]]) h proxy f f' f''. (All2 c xss, Prod h ~ (NP :: ([k] -> Type) -> [[k]] -> Type), HAp h) => proxy c -> (forall (xs :: [k]). All c xs => f xs -> f' xs -> f'' xs) -> Prod h f xss -> h f' xss -> h f'' xss
- hcliftA3' :: forall {k} (c :: k -> Constraint) (xss :: [[k]]) h proxy f f' f'' f'''. (All2 c xss, Prod h ~ (NP :: ([k] -> Type) -> [[k]] -> Type), HAp h) => proxy c -> (forall (xs :: [k]). All c xs => f xs -> f' xs -> f'' xs -> f''' xs) -> Prod h f xss -> Prod h f' xss -> h f'' xss -> h f''' xss
- compare_NS :: forall {k} r f g (xs :: [k]). r -> (forall (x :: k). f x -> g x -> r) -> r -> NS f xs -> NS g xs -> r
- ccompare_NS :: forall {k} c proxy r f g (xs :: [k]). All c xs => proxy c -> r -> (forall (x :: k). c x => f x -> g x -> r) -> r -> NS f xs -> NS g xs -> r
- compare_SOP :: forall {k} r (f :: k -> Type) (g :: k -> Type) (xss :: [[k]]). r -> (forall (xs :: [k]). NP f xs -> NP g xs -> r) -> r -> SOP f xss -> SOP g xss -> r
- ccompare_SOP :: forall {k} (c :: k -> Constraint) proxy r (f :: k -> Type) (g :: k -> Type) (xss :: [[k]]). All2 c xss => proxy c -> r -> (forall (xs :: [k]). All c xs => NP f xs -> NP g xs -> r) -> r -> SOP f xss -> SOP g xss -> r
- type family CollapseTo (h :: (k -> Type) -> l -> Type) x
- class HCollapse (h :: (k -> Type) -> l -> Type) where
  - hcollapse :: forall (xs :: l) a. SListIN h xs => h (K a :: k -> Type) xs -> CollapseTo h a
- class HTraverse_ (h :: (k -> Type) -> l -> Type) where
  - hctraverse_ :: forall c (xs :: l) g proxy f. (AllN h c xs, Applicative g) => proxy c -> (forall (a :: k). c a => f a -> g ()) -> h f xs -> g ()
  - htraverse_ :: forall (xs :: l) g f. (SListIN h xs, Applicative g) => (forall (a :: k). f a -> g ()) -> h f xs -> g ()
- hcfoldMap :: forall {k} {l} h c (xs :: l) m proxy f. (HTraverse_ h, AllN h c xs, Monoid m) => proxy c -> (forall (a :: k). c a => f a -> m) -> h f xs -> m
- hcfor_ :: forall {k} {l} h c (xs :: l) g proxy f. (HTraverse_ h, AllN h c xs, Applicative g) => proxy c -> h f xs -> (forall (a :: k). c a => f a -> g ()) -> g ()
- class HAp h => HSequence (h :: (k -> Type) -> l -> Type) where
  - hsequence' :: forall (xs :: l) f (g :: k -> Type). (SListIN h xs, Applicative f) => h (f :.: g) xs -> f (h g xs)
  - hctraverse' :: forall c (xs :: l) g proxy f f'. (AllN h c xs, Applicative g) => proxy c -> (forall (a :: k). c a => f a -> g (f' a)) -> h f xs -> g (h f' xs)
  - htraverse' :: forall (xs :: l) g f f'. (SListIN h xs, Applicative g) => (forall (a :: k). f a -> g (f' a)) -> h f xs -> g (h f' xs)
- hsequence :: forall {l} h (xs :: l) f. (SListIN h xs, SListIN (Prod h) xs, HSequence h, Applicative f) => h f xs -> f (h I xs)
- hsequenceK :: forall {k} {l} h (xs :: l) f a. (SListIN h xs, SListIN (Prod h) xs, Applicative f, HSequence h) => h (K (f a) :: k -> Type) xs -> f (h (K a :: k -> Type) xs)
- hctraverse :: forall {l} h c (xs :: l) g proxy f. (HSequence h, AllN h c xs, Applicative g) => proxy c -> (forall a. c a => f a -> g a) -> h f xs -> g (h I xs)
- hcfor :: forall {l} h c (xs :: l) g proxy f. (HSequence h, AllN h c xs, Applicative g) => proxy c -> h f xs -> (forall a. c a => f a -> g a) -> g (h I xs)
- class HExpand (h :: (k -> Type) -> l -> Type) where
  - hexpand :: forall (xs :: l) f. SListIN (Prod h) xs => (forall (x :: k). f x) -> h f xs -> Prod h f xs
  - hcexpand :: forall c (xs :: l) proxy f. AllN (Prod h) c xs => proxy c -> (forall (x :: k). c x => f x) -> h f xs -> Prod h f xs
- class ((Same h1 :: (k2 -> Type) -> l2 -> Type) ~ h2, (Same h2 :: (k1 -> Type) -> l1 -> Type) ~ h1) => HTrans (h1 :: (k1 -> Type) -> l1 -> Type) (h2 :: (k2 -> Type) -> l2 -> Type) where
  - htrans :: forall c (xs :: l1) (ys :: l2) proxy f g. AllZipN (Prod h1) c xs ys => proxy c -> (forall (x :: k1) (y :: k2). c x y => f x -> g y) -> h1 f xs -> h2 g ys
  - hcoerce :: forall (f :: k1 -> Type) (g :: k2 -> Type) (xs :: l1) (ys :: l2). AllZipN (Prod h1) (LiftedCoercible f g) xs ys => h1 f xs -> h2 g ys
- hfromI :: forall {l1} {k2} {l2} h1 (f :: k2 -> Type) (xs :: l1) (ys :: l2) h2. (AllZipN (Prod h1) (LiftedCoercible I f) xs ys, HTrans h1 h2) => h1 I xs -> h2 f ys
- htoI :: forall {k1} {l1} {l2} h1 (f :: k1 -> Type) (xs :: l1) (ys :: l2) h2. (AllZipN (Prod h1) (LiftedCoercible f I) xs ys, HTrans h1 h2) => h1 f xs -> h2 I ys
- fromList :: forall {k} (xs :: [k]) a. SListI xs => [a] -> Maybe (NP (K a :: k -> Type) xs)
- newtype K a (b :: k) = K a
- unK :: forall {k} a (b :: k). K a b -> a
- newtype I a = I a
- unI :: I a -> a
- newtype ((f :: l -> Type) :.: (g :: k -> l)) (p :: k) = Comp (f (g p))
- unComp :: forall {l} {k} f (g :: k -> l) (p :: k). (f :.: g) p -> f (g p)
- mapII :: (a -> b) -> I a -> I b
- mapIK :: forall {k} a b (c :: k). (a -> b) -> I a -> K b c
- mapKI :: forall {k} a b (c :: k). (a -> b) -> K a c -> I b
- mapKK :: forall {k1} {k2} a b (c :: k1) (d :: k2). (a -> b) -> K a c -> K b d
- mapIII :: (a -> b -> c) -> I a -> I b -> I c
- mapIIK :: forall {k} a b c (d :: k). (a -> b -> c) -> I a -> I b -> K c d
- mapIKI :: forall {k} a b c (d :: k). (a -> b -> c) -> I a -> K b d -> I c
- mapIKK :: forall {k1} {k2} a b c (d :: k1) (e :: k2). (a -> b -> c) -> I a -> K b d -> K c e
- mapKII :: forall {k} a b c (d :: k). (a -> b -> c) -> K a d -> I b -> I c
- mapKIK :: forall {k1} {k2} a b c (d :: k1) (e :: k2). (a -> b -> c) -> K a d -> I b -> K c e
- mapKKI :: forall {k1} {k2} a b c (d :: k1) (e :: k2). (a -> b -> c) -> K a d -> K b e -> I c
- mapKKK :: forall {k1} {k2} {k3} a b c (d :: k1) (e :: k2) (f :: k3). (a -> b -> c) -> K a d -> K b e -> K c f
- class (AllF c xs, SListI xs) => All (c :: k -> Constraint) (xs :: [k])
- type All2 (c :: k -> Constraint) = All (All c)
- cpara_SList :: All c xs => proxy c -> r ('[] :: [k]) -> (forall (y :: k) (ys :: [k]). (c y, All c ys) => r ys -> r (y ': ys)) -> r xs
- ccase_SList :: forall {a} c (xs :: [a]) proxy r. All c xs => proxy c -> r ('[] :: [a]) -> (forall (y :: a) (ys :: [a]). (c y, All c ys) => r (y ': ys)) -> r xs
- class (SListI xs, SListI ys, SameShapeAs xs ys, SameShapeAs ys xs, AllZipF c xs ys) => AllZip (c :: a -> b -> Constraint) (xs :: [a]) (ys :: [b])
- class (AllZipF (AllZip f) xss yss, SListI xss, SListI yss, SameShapeAs xss yss, SameShapeAs yss xss) => AllZip2 (f :: a -> b -> Constraint) (xss :: [[a]]) (yss :: [[b]])
- type family AllN (h :: (k -> Type) -> l -> Type) (c :: k -> Constraint) :: l -> Constraint
- type family AllZipN (h :: (k -> Type) -> l -> Type) (c :: k1 -> k2 -> Constraint) :: l1 -> l2 -> Constraint
- class f (g x) => Compose (f :: k -> Constraint) (g :: k1 -> k) (x :: k1)
- class (f x, g x) => And (f :: k -> Constraint) (g :: k -> Constraint) (x :: k)
- class Top (x :: k)
- class Coercible (f x) (g y) => LiftedCoercible (f :: k -> k1) (g :: k2 -> k1) (x :: k) (y :: k2)
- type family SameShapeAs (xs :: [a]) (ys :: [b]) where ...
- data SList (a :: [k]) where
  - SNil :: forall {k}. SList ('[] :: [k])
  - SCons :: forall {k} (xs :: [k]) (x :: k). SListI xs => SList (x ': xs)
- type SListI = All (Top :: k -> Constraint)
- type SListI2 = All (SListI :: [k] -> Constraint)
- sList :: forall {k} (xs :: [k]). SListI xs => SList xs
- para_SList :: forall {a} (xs :: [a]) r. SListI xs => r ('[] :: [a]) -> (forall (y :: a) (ys :: [a]). SListI ys => r ys -> r (y ': ys)) -> r xs
- case_SList :: forall {a} (xs :: [a]) r. SListI xs => r ('[] :: [a]) -> (forall (y :: a) (ys :: [a]). SListI ys => r (y ': ys)) -> r xs
- data Shape (a :: [k]) where
  - ShapeNil :: forall {k}. Shape ('[] :: [k])
  - ShapeCons :: forall {k} (xs :: [k]) (x :: k). SListI xs => Shape xs -> Shape (x ': xs)
- shape :: forall k (xs :: [k]). SListI xs => Shape xs
- lengthSList :: forall k (xs :: [k]) proxy. SListI xs => proxy xs -> Int
- data Proxy (t :: k) = Proxy

# n-ary datatypes

data NP (a :: k -> Type) (b :: [k]) where #

An n-ary product.

The product is parameterized by a type constructor `f` and indexed by a type-level list `xs`. The length of the list determines the number of elements in the product, and if the `i`-th element of the list is of type `x`, then the `i`-th element of the product is of type `f x`.

The constructor names are chosen to resemble the names of the list constructors.

Two common instantiations of `f` are the identity functor `I` and the constant functor `K`. For `I`, the product becomes a heterogeneous list, where the type-level list describes the types of its components. For ``K` a`, the product becomes a homogeneous list, where the contents of the type-level list are ignored, but its length still specifies the number of elements.

In the context of the SOP approach to generic programming, an n-ary product describes the structure of the arguments of a single data constructor.

Examples:

    I 'x'    :* I True  :* Nil  ::  NP I       '[ Char, Bool ]
    K 0      :* K 1     :* Nil  ::  NP (K Int) '[ Char, Bool ]
    Just 'x' :* Nothing :* Nil  ::  NP Maybe   '[ Char, Bool ]

Constructors

Nil :: forall {k} (a :: k -> Type). NP a ('[] :: [k]) |
(:*) :: forall {k} (a :: k -> Type) (x :: k) (xs :: [k]). a x -> NP a xs -> NP a (x ': xs) infixr 5 |

#### Instances

Instances details

HTrans (NP :: (k1 -> Type) -> [k1] -> Type) (NP :: (k2 -> Type) -> [k2] -> Type) # |

Instance details

Defined in Data.SOP.NP

Methods

htrans :: forall c (xs :: [k1]) (ys :: [k2]) proxy f g. AllZipN (Prod (NP :: (k1 -> Type) -> [k1] -> Type)) c xs ys => proxy c -> (forall (x :: k1) (y :: k2). c x y => f x -> g y) -> NP f xs -> NP g ys #

hcoerce :: forall (f :: k1 -> Type) (g :: k2 -> Type) (xs :: [k1]) (ys :: [k2]). AllZipN (Prod (NP :: (k1 -> Type) -> [k1] -> Type)) (LiftedCoercible f g) xs ys => NP f xs -> NP g ys #

HAp (NP :: (k -> Type) -> [k] -> Type) # |
Instance details Defined in Data.SOP.NP Methods hap :: forall (f :: k -> Type) (g :: k -> Type) (xs :: [k]). Prod (NP :: (k -> Type) -> [k] -> Type) (f -.-> g) xs -> NP f xs -> NP g xs #
HCollapse (NP :: (k -> Type) -> [k] -> Type) # |
Instance details Defined in Data.SOP.NP Methods hcollapse :: forall (xs :: [k]) a. SListIN (NP :: (k -> Type) -> [k] -> Type) xs => NP (K a :: k -> Type) xs -> CollapseTo (NP :: (k -> Type) -> [k] -> Type) a #
HPure (NP :: (k -> Type) -> [k] -> Type) # |
Instance details Defined in Data.SOP.NP Methods hpure :: forall (xs :: [k]) f. SListIN (NP :: (k -> Type) -> [k] -> Type) xs => (forall (a :: k). f a) -> NP f xs # hcpure :: forall c (xs :: [k]) proxy f. AllN (NP :: (k -> Type) -> [k] -> Type) c xs => proxy c -> (forall (a :: k). c a => f a) -> NP f xs #
HSequence (NP :: (k -> Type) -> [k] -> Type) # |

Instance details

Defined in Data.SOP.NP

Methods

hsequence' :: forall (xs :: [k]) f (g :: k -> Type). (SListIN (NP :: (k -> Type) -> [k] -> Type) xs, Applicative f) => NP (f :.: g) xs -> f (NP g xs) #

hctraverse' :: forall c (xs :: [k]) g proxy f f'. (AllN (NP :: (k -> Type) -> [k] -> Type) c xs, Applicative g) => proxy c -> (forall (a :: k). c a => f a -> g (f' a)) -> NP f xs -> g (NP f' xs) #

htraverse' :: forall (xs :: [k]) g f f'. (SListIN (NP :: (k -> Type) -> [k] -> Type) xs, Applicative g) => (forall (a :: k). f a -> g (f' a)) -> NP f xs -> g (NP f' xs) #

HTraverse_ (NP :: (k -> Type) -> [k] -> Type) # |
Instance details Defined in Data.SOP.NP Methods hctraverse_ :: forall c (xs :: [k]) g proxy f. (AllN (NP :: (k -> Type) -> [k] -> Type) c xs, Applicative g) => proxy c -> (forall (a :: k). c a => f a -> g ()) -> NP f xs -> g () # htraverse_ :: forall (xs :: [k]) g f. (SListIN (NP :: (k -> Type) -> [k] -> Type) xs, Applicative g) => (forall (a :: k). f a -> g ()) -> NP f xs -> g () #
All (Compose NFData f) xs => NFData (NP f xs) # | Since: 0.2.5.0
Instance details Defined in Data.SOP.NP Methods rnf :: NP f xs -> () #
(All (Compose Monoid f) xs, All (Compose Semigroup f) xs) => Monoid (NP f xs) # | Since: 0.4.0.0
Instance details Defined in Data.SOP.NP Methods mempty :: NP f xs # mappend :: NP f xs -> NP f xs -> NP f xs # mconcat :: [NP f xs] -> NP f xs #
All (Compose Semigroup f) xs => Semigroup (NP f xs) # | Since: 0.4.0.0
Instance details Defined in Data.SOP.NP Methods (<>) :: NP f xs -> NP f xs -> NP f xs # sconcat :: NonEmpty (NP f xs) -> NP f xs # stimes :: Integral b => b -> NP f xs -> NP f xs #
All (Compose Show f) xs => Show (NP f xs) # |
Instance details Defined in Data.SOP.NP Methods showsPrec :: Int -> NP f xs -> ShowS # show :: NP f xs -> String # showList :: [NP f xs] -> ShowS #
All (Compose Eq f) xs => Eq (NP f xs) # |
Instance details Defined in Data.SOP.NP Methods (==) :: NP f xs -> NP f xs -> Bool # (/=) :: NP f xs -> NP f xs -> Bool #
(All (Compose Eq f) xs, All (Compose Ord f) xs) => Ord (NP f xs) # |
Instance details Defined in Data.SOP.NP Methods compare :: NP f xs -> NP f xs -> Ordering # (<) :: NP f xs -> NP f xs -> Bool # (<=) :: NP f xs -> NP f xs -> Bool # (>) :: NP f xs -> NP f xs -> Bool # (>=) :: NP f xs -> NP f xs -> Bool # max :: NP f xs -> NP f xs -> NP f xs # min :: NP f xs -> NP f xs -> NP f xs #
type AllZipN (NP :: (k -> Type) -> [k] -> Type) (c :: a -> b -> Constraint) # |
Instance details Defined in Data.SOP.NP type AllZipN (NP :: (k -> Type) -> [k] -> Type) (c :: a -> b -> Constraint) = AllZip c
type Same (NP :: (k1 -> Type) -> [k1] -> Type) # |
Instance details Defined in Data.SOP.NP type Same (NP :: (k1 -> Type) -> [k1] -> Type) = NP :: (k2 -> Type) -> [k2] -> Type
type Prod (NP :: (k -> Type) -> [k] -> Type) # |
Instance details Defined in Data.SOP.NP type Prod (NP :: (k -> Type) -> [k] -> Type) = NP :: (k -> Type) -> [k] -> Type
type UnProd (NP :: (k -> Type) -> [k] -> Type) # |
Instance details Defined in Data.SOP.NS type UnProd (NP :: (k -> Type) -> [k] -> Type) = NS :: (k -> Type) -> [k] -> Type
type SListIN (NP :: (k -> Type) -> [k] -> Type) # |
Instance details Defined in Data.SOP.NP type SListIN (NP :: (k -> Type) -> [k] -> Type) = SListI :: [k] -> Constraint
type CollapseTo (NP :: (k -> Type) -> [k] -> Type) a # |
Instance details Defined in Data.SOP.NP type CollapseTo (NP :: (k -> Type) -> [k] -> Type) a = [a]
type AllN (NP :: (k -> Type) -> [k] -> Type) (c :: k -> Constraint) # |
Instance details Defined in Data.SOP.NP type AllN (NP :: (k -> Type) -> [k] -> Type) (c :: k -> Constraint) = All c

data NS (a :: k -> Type) (b :: [k]) where #

An n-ary sum.

The sum is parameterized by a type constructor `f` and indexed by a type-level list `xs`. The length of the list determines the number of choices in the sum and if the `i`-th element of the list is of type `x`, then the `i`-th choice of the sum is of type `f x`.

The constructor names are chosen to resemble Peano-style natural numbers, i.e., `Z` is for "zero", and `S` is for "successor". Chaining `S` and `Z` chooses the corresponding component of the sum.

Examples:

    Z         :: f x -> NS f (x ': xs)
    S . Z     :: f y -> NS f (x ': y ': xs)
    S . S . Z :: f z -> NS f (x ': y ': z ': xs)
    ...

Note that empty sums (indexed by an empty list) have no non-bottom elements.

Two common instantiations of `f` are the identity functor `I` and the constant functor `K`. For `I`, the sum becomes a direct generalization of the `Either` type to arbitrarily many choices. For ``K` a`, the result is a homogeneous choice type, where the contents of the type-level list are ignored, but its length specifies the number of options.

In the context of the SOP approach to generic programming, an n-ary sum describes the top-level structure of a datatype, which is a choice between all of its constructors.

Examples:

    Z (I 'x')      :: NS I       '[ Char, Bool ]
    S (Z (I True)) :: NS I       '[ Char, Bool ]
    S (Z (K 1))    :: NS (K Int) '[ Char, Bool ]

Constructors

Z :: forall {k} (a :: k -> Type) (x :: k) (xs :: [k]). a x -> NS a (x ': xs) |
S :: forall {k} (a :: k -> Type) (xs :: [k]) (x :: k). NS a xs -> NS a (x ': xs) |

#### Instances

Instances details

HTrans (NS :: (k1 -> Type) -> [k1] -> Type) (NS :: (k2 -> Type) -> [k2] -> Type) # |

Instance details

Defined in Data.SOP.NS

Methods

htrans :: forall c (xs :: [k1]) (ys :: [k2]) proxy f g. AllZipN (Prod (NS :: (k1 -> Type) -> [k1] -> Type)) c xs ys => proxy c -> (forall (x :: k1) (y :: k2). c x y => f x -> g y) -> NS f xs -> NS g ys #

hcoerce :: forall (f :: k1 -> Type) (g :: k2 -> Type) (xs :: [k1]) (ys :: [k2]). AllZipN (Prod (NS :: (k1 -> Type) -> [k1] -> Type)) (LiftedCoercible f g) xs ys => NS f xs -> NS g ys #

HAp (NS :: (k -> Type) -> [k] -> Type) # |
Instance details Defined in Data.SOP.NS Methods hap :: forall (f :: k -> Type) (g :: k -> Type) (xs :: [k]). Prod (NS :: (k -> Type) -> [k] -> Type) (f -.-> g) xs -> NS f xs -> NS g xs #
HApInjs (NS :: (k -> Type) -> [k] -> Type) # |
Instance details Defined in Data.SOP.NS Methods hapInjs :: forall (xs :: [k]) (f :: k -> Type). SListIN (NS :: (k -> Type) -> [k] -> Type) xs => Prod (NS :: (k -> Type) -> [k] -> Type) f xs -> [NS f xs] #
HCollapse (NS :: (k -> Type) -> [k] -> Type) # |
Instance details Defined in Data.SOP.NS Methods hcollapse :: forall (xs :: [k]) a. SListIN (NS :: (k -> Type) -> [k] -> Type) xs => NS (K a :: k -> Type) xs -> CollapseTo (NS :: (k -> Type) -> [k] -> Type) a #
HExpand (NS :: (k -> Type) -> [k] -> Type) # |

Instance details

Defined in Data.SOP.NS

Methods

hexpand :: forall (xs :: [k]) f. SListIN (Prod (NS :: (k -> Type) -> [k] -> Type)) xs => (forall (x :: k). f x) -> NS f xs -> Prod (NS :: (k -> Type) -> [k] -> Type) f xs #

hcexpand :: forall c (xs :: [k]) proxy f. AllN (Prod (NS :: (k -> Type) -> [k] -> Type)) c xs => proxy c -> (forall (x :: k). c x => f x) -> NS f xs -> Prod (NS :: (k -> Type) -> [k] -> Type) f xs #

HIndex (NS :: (k -> Type) -> [k] -> Type) # |
Instance details Defined in Data.SOP.NS Methods hindex :: forall (f :: k -> Type) (xs :: [k]). NS f xs -> Int #
HSequence (NS :: (k -> Type) -> [k] -> Type) # |

Instance details

Defined in Data.SOP.NS

Methods

hsequence' :: forall (xs :: [k]) f (g :: k -> Type). (SListIN (NS :: (k -> Type) -> [k] -> Type) xs, Applicative f) => NS (f :.: g) xs -> f (NS g xs) #

hctraverse' :: forall c (xs :: [k]) g proxy f f'. (AllN (NS :: (k -> Type) -> [k] -> Type) c xs, Applicative g) => proxy c -> (forall (a :: k). c a => f a -> g (f' a)) -> NS f xs -> g (NS f' xs) #

htraverse' :: forall (xs :: [k]) g f f'. (SListIN (NS :: (k -> Type) -> [k] -> Type) xs, Applicative g) => (forall (a :: k). f a -> g (f' a)) -> NS f xs -> g (NS f' xs) #

HTraverse_ (NS :: (k -> Type) -> [k] -> Type) # |
Instance details Defined in Data.SOP.NS Methods hctraverse_ :: forall c (xs :: [k]) g proxy f. (AllN (NS :: (k -> Type) -> [k] -> Type) c xs, Applicative g) => proxy c -> (forall (a :: k). c a => f a -> g ()) -> NS f xs -> g () # htraverse_ :: forall (xs :: [k]) g f. (SListIN (NS :: (k -> Type) -> [k] -> Type) xs, Applicative g) => (forall (a :: k). f a -> g ()) -> NS f xs -> g () #
All (Compose NFData f) xs => NFData (NS f xs) # | Since: 0.2.5.0
Instance details Defined in Data.SOP.NS Methods rnf :: NS f xs -> () #
All (Compose Show f) xs => Show (NS f xs) # |
Instance details Defined in Data.SOP.NS Methods showsPrec :: Int -> NS f xs -> ShowS # show :: NS f xs -> String # showList :: [NS f xs] -> ShowS #
All (Compose Eq f) xs => Eq (NS f xs) # |
Instance details Defined in Data.SOP.NS Methods (==) :: NS f xs -> NS f xs -> Bool # (/=) :: NS f xs -> NS f xs -> Bool #
(All (Compose Eq f) xs, All (Compose Ord f) xs) => Ord (NS f xs) # |
Instance details Defined in Data.SOP.NS Methods compare :: NS f xs -> NS f xs -> Ordering # (<) :: NS f xs -> NS f xs -> Bool # (<=) :: NS f xs -> NS f xs -> Bool # (>) :: NS f xs -> NS f xs -> Bool # (>=) :: NS f xs -> NS f xs -> Bool # max :: NS f xs -> NS f xs -> NS f xs # min :: NS f xs -> NS f xs -> NS f xs #
type Same (NS :: (k1 -> Type) -> [k1] -> Type) # |
Instance details Defined in Data.SOP.NS type Same (NS :: (k1 -> Type) -> [k1] -> Type) = NS :: (k2 -> Type) -> [k2] -> Type
type Prod (NS :: (k -> Type) -> [k] -> Type) # |
Instance details Defined in Data.SOP.NS type Prod (NS :: (k -> Type) -> [k] -> Type) = NP :: (k -> Type) -> [k] -> Type
type SListIN (NS :: (k -> Type) -> [k] -> Type) # |
Instance details Defined in Data.SOP.NS type SListIN (NS :: (k -> Type) -> [k] -> Type) = SListI :: [k] -> Constraint
type CollapseTo (NS :: (k -> Type) -> [k] -> Type) a # |
Instance details Defined in Data.SOP.NS type CollapseTo (NS :: (k -> Type) -> [k] -> Type) a = a
type AllN (NS :: (k -> Type) -> [k] -> Type) (c :: k -> Constraint) # |
Instance details Defined in Data.SOP.NS type AllN (NS :: (k -> Type) -> [k] -> Type) (c :: k -> Constraint) = All c

newtype SOP (f :: k -> Type) (xss :: [[k]]) #

A sum of products.

This is a 'newtype' for an `NS` of an `NP`. The elements of the (inner) products are applications of the parameter `f`. The type `SOP` is indexed by the list of lists that determines the sizes of both the (outer) sum and all the (inner) products, as well as the types of all the elements of the inner products.

A ``SOP` `I`` reflects the structure of a normal Haskell datatype. The sum structure represents the choice between the different constructors, the product structure represents the arguments of each constructor.

Constructors

SOP (NS (NP f) xss) |

#### Instances

Instances details

HTrans (SOP :: (k1 -> Type) -> [[k1]] -> Type) (SOP :: (k2 -> Type) -> [[k2]] -> Type) # |

Instance details

Defined in Data.SOP.NS

Methods

htrans :: forall c (xs :: [[k1]]) (ys :: [[k2]]) proxy f g. AllZipN (Prod (SOP :: (k1 -> Type) -> [[k1]] -> Type)) c xs ys => proxy c -> (forall (x :: k1) (y :: k2). c x y => f x -> g y) -> SOP f xs -> SOP g ys #

hcoerce :: forall (f :: k1 -> Type) (g :: k2 -> Type) (xs :: [[k1]]) (ys :: [[k2]]). AllZipN (Prod (SOP :: (k1 -> Type) -> [[k1]] -> Type)) (LiftedCoercible f g) xs ys => SOP f xs -> SOP g ys #

HAp (SOP :: (k -> Type) -> [[k]] -> Type) # |
Instance details Defined in Data.SOP.NS Methods hap :: forall (f :: k -> Type) (g :: k -> Type) (xs :: [[k]]). Prod (SOP :: (k -> Type) -> [[k]] -> Type) (f -.-> g) xs -> SOP f xs -> SOP g xs #
HApInjs (SOP :: (k -> Type) -> [[k]] -> Type) # |
Instance details Defined in Data.SOP.NS Methods hapInjs :: forall (xs :: [[k]]) (f :: k -> Type). SListIN (SOP :: (k -> Type) -> [[k]] -> Type) xs => Prod (SOP :: (k -> Type) -> [[k]] -> Type) f xs -> [SOP f xs] #
HCollapse (SOP :: (k -> Type) -> [[k]] -> Type) # |
Instance details Defined in Data.SOP.NS Methods hcollapse :: forall (xs :: [[k]]) a. SListIN (SOP :: (k -> Type) -> [[k]] -> Type) xs => SOP (K a :: k -> Type) xs -> CollapseTo (SOP :: (k -> Type) -> [[k]] -> Type) a #
HExpand (SOP :: (k -> Type) -> [[k]] -> Type) # |

Instance details

Defined in Data.SOP.NS

Methods

hexpand :: forall (xs :: [[k]]) f. SListIN (Prod (SOP :: (k -> Type) -> [[k]] -> Type)) xs => (forall (x :: k). f x) -> SOP f xs -> Prod (SOP :: (k -> Type) -> [[k]] -> Type) f xs #

hcexpand :: forall c (xs :: [[k]]) proxy f. AllN (Prod (SOP :: (k -> Type) -> [[k]] -> Type)) c xs => proxy c -> (forall (x :: k). c x => f x) -> SOP f xs -> Prod (SOP :: (k -> Type) -> [[k]] -> Type) f xs #

HIndex (SOP :: (k -> Type) -> [[k]] -> Type) # |
Instance details Defined in Data.SOP.NS Methods hindex :: forall (f :: k -> Type) (xs :: [[k]]). SOP f xs -> Int #
HSequence (SOP :: (k -> Type) -> [[k]] -> Type) # |

Instance details

Defined in Data.SOP.NS

Methods

hsequence' :: forall (xs :: [[k]]) f (g :: k -> Type). (SListIN (SOP :: (k -> Type) -> [[k]] -> Type) xs, Applicative f) => SOP (f :.: g) xs -> f (SOP g xs) #

hctraverse' :: forall c (xs :: [[k]]) g proxy f f'. (AllN (SOP :: (k -> Type) -> [[k]] -> Type) c xs, Applicative g) => proxy c -> (forall (a :: k). c a => f a -> g (f' a)) -> SOP f xs -> g (SOP f' xs) #

htraverse' :: forall (xs :: [[k]]) g f f'. (SListIN (SOP :: (k -> Type) -> [[k]] -> Type) xs, Applicative g) => (forall (a :: k). f a -> g (f' a)) -> SOP f xs -> g (SOP f' xs) #

HTraverse_ (SOP :: (k -> Type) -> [[k]] -> Type) # |
Instance details Defined in Data.SOP.NS Methods hctraverse_ :: forall c (xs :: [[k]]) g proxy f. (AllN (SOP :: (k -> Type) -> [[k]] -> Type) c xs, Applicative g) => proxy c -> (forall (a :: k). c a => f a -> g ()) -> SOP f xs -> g () # htraverse_ :: forall (xs :: [[k]]) g f. (SListIN (SOP :: (k -> Type) -> [[k]] -> Type) xs, Applicative g) => (forall (a :: k). f a -> g ()) -> SOP f xs -> g () #
NFData (NS (NP f) xss) => NFData (SOP f xss) # | Since: 0.2.5.0
Instance details Defined in Data.SOP.NS Methods rnf :: SOP f xss -> () #
Show (NS (NP f) xss) => Show (SOP f xss) # |
Instance details Defined in Data.SOP.NS Methods showsPrec :: Int -> SOP f xss -> ShowS # show :: SOP f xss -> String # showList :: [SOP f xss] -> ShowS #
Eq (NS (NP f) xss) => Eq (SOP f xss) # |
Instance details Defined in Data.SOP.NS Methods (==) :: SOP f xss -> SOP f xss -> Bool # (/=) :: SOP f xss -> SOP f xss -> Bool #
Ord (NS (NP f) xss) => Ord (SOP f xss) # |
Instance details Defined in Data.SOP.NS Methods compare :: SOP f xss -> SOP f xss -> Ordering # (<) :: SOP f xss -> SOP f xss -> Bool # (<=) :: SOP f xss -> SOP f xss -> Bool # (>) :: SOP f xss -> SOP f xss -> Bool # (>=) :: SOP f xss -> SOP f xss -> Bool # max :: SOP f xss -> SOP f xss -> SOP f xss # min :: SOP f xss -> SOP f xss -> SOP f xss #
type Same (SOP :: (k1 -> Type) -> [[k1]] -> Type) # |
Instance details Defined in Data.SOP.NS type Same (SOP :: (k1 -> Type) -> [[k1]] -> Type) = SOP :: (k2 -> Type) -> [[k2]] -> Type
type Prod (SOP :: (k -> Type) -> [[k]] -> Type) # |
Instance details Defined in Data.SOP.NS type Prod (SOP :: (k -> Type) -> [[k]] -> Type) = POP :: (k -> Type) -> [[k]] -> Type
type SListIN (SOP :: (k -> Type) -> [[k]] -> Type) # |
Instance details Defined in Data.SOP.NS type SListIN (SOP :: (k -> Type) -> [[k]] -> Type) = SListI2 :: [[k]] -> Constraint
type CollapseTo (SOP :: (k -> Type) -> [[k]] -> Type) a # |
Instance details Defined in Data.SOP.NS type CollapseTo (SOP :: (k -> Type) -> [[k]] -> Type) a = [a]
type AllN (SOP :: (k -> Type) -> [[k]] -> Type) (c :: k -> Constraint) # |
Instance details Defined in Data.SOP.NS type AllN (SOP :: (k -> Type) -> [[k]] -> Type) (c :: k -> Constraint) = All2 c

unSOP :: forall {k} (f :: k -> Type) (xss :: [[k]]). SOP f xss -> NS (NP f) xss #

Unwrap a sum of products.

newtype POP (f :: k -> Type) (xss :: [[k]]) #

A product of products.

This is a 'newtype' for an `NP` of an `NP`. The elements of the inner products are applications of the parameter `f`. The type `POP` is indexed by the list of lists that determines the lengths of both the outer and all the inner products, as well as the types of all the elements of the inner products.

A `POP` is reminiscent of a two-dimensional table (but the inner lists can all be of different length). In the context of the SOP approach to generic programming, a `POP` is useful to represent information that is available for all arguments of all constructors of a datatype.

Constructors

POP (NP (NP f) xss) |

#### Instances

Instances details

HTrans (POP :: (k1 -> Type) -> [[k1]] -> Type) (POP :: (k2 -> Type) -> [[k2]] -> Type) # |

Instance details

Defined in Data.SOP.NP

Methods

htrans :: forall c (xs :: [[k1]]) (ys :: [[k2]]) proxy f g. AllZipN (Prod (POP :: (k1 -> Type) -> [[k1]] -> Type)) c xs ys => proxy c -> (forall (x :: k1) (y :: k2). c x y => f x -> g y) -> POP f xs -> POP g ys #

hcoerce :: forall (f :: k1 -> Type) (g :: k2 -> Type) (xs :: [[k1]]) (ys :: [[k2]]). AllZipN (Prod (POP :: (k1 -> Type) -> [[k1]] -> Type)) (LiftedCoercible f g) xs ys => POP f xs -> POP g ys #

HAp (POP :: (k -> Type) -> [[k]] -> Type) # |
Instance details Defined in Data.SOP.NP Methods hap :: forall (f :: k -> Type) (g :: k -> Type) (xs :: [[k]]). Prod (POP :: (k -> Type) -> [[k]] -> Type) (f -.-> g) xs -> POP f xs -> POP g xs #
HCollapse (POP :: (k -> Type) -> [[k]] -> Type) # |
Instance details Defined in Data.SOP.NP Methods hcollapse :: forall (xs :: [[k]]) a. SListIN (POP :: (k -> Type) -> [[k]] -> Type) xs => POP (K a :: k -> Type) xs -> CollapseTo (POP :: (k -> Type) -> [[k]] -> Type) a #
HPure (POP :: (k -> Type) -> [[k]] -> Type) # |
Instance details Defined in Data.SOP.NP Methods hpure :: forall (xs :: [[k]]) f. SListIN (POP :: (k -> Type) -> [[k]] -> Type) xs => (forall (a :: k). f a) -> POP f xs # hcpure :: forall c (xs :: [[k]]) proxy f. AllN (POP :: (k -> Type) -> [[k]] -> Type) c xs => proxy c -> (forall (a :: k). c a => f a) -> POP f xs #
HSequence (POP :: (k -> Type) -> [[k]] -> Type) # |

Instance details

Defined in Data.SOP.NP

Methods

hsequence' :: forall (xs :: [[k]]) f (g :: k -> Type). (SListIN (POP :: (k -> Type) -> [[k]] -> Type) xs, Applicative f) => POP (f :.: g) xs -> f (POP g xs) #

hctraverse' :: forall c (xs :: [[k]]) g proxy f f'. (AllN (POP :: (k -> Type) -> [[k]] -> Type) c xs, Applicative g) => proxy c -> (forall (a :: k). c a => f a -> g (f' a)) -> POP f xs -> g (POP f' xs) #

htraverse' :: forall (xs :: [[k]]) g f f'. (SListIN (POP :: (k -> Type) -> [[k]] -> Type) xs, Applicative g) => (forall (a :: k). f a -> g (f' a)) -> POP f xs -> g (POP f' xs) #

HTraverse_ (POP :: (k -> Type) -> [[k]] -> Type) # |
Instance details Defined in Data.SOP.NP Methods hctraverse_ :: forall c (xs :: [[k]]) g proxy f. (AllN (POP :: (k -> Type) -> [[k]] -> Type) c xs, Applicative g) => proxy c -> (forall (a :: k). c a => f a -> g ()) -> POP f xs -> g () # htraverse_ :: forall (xs :: [[k]]) g f. (SListIN (POP :: (k -> Type) -> [[k]] -> Type) xs, Applicative g) => (forall (a :: k). f a -> g ()) -> POP f xs -> g () #
NFData (NP (NP f) xss) => NFData (POP f xss) # | Since: 0.2.5.0
Instance details Defined in Data.SOP.NP Methods rnf :: POP f xss -> () #
Monoid (NP (NP f) xss) => Monoid (POP f xss) # | Since: 0.4.0.0
Instance details Defined in Data.SOP.NP Methods mempty :: POP f xss # mappend :: POP f xss -> POP f xss -> POP f xss # mconcat :: [POP f xss] -> POP f xss #
Semigroup (NP (NP f) xss) => Semigroup (POP f xss) # | Since: 0.4.0.0
Instance details Defined in Data.SOP.NP Methods (<>) :: POP f xss -> POP f xss -> POP f xss # sconcat :: NonEmpty (POP f xss) -> POP f xss # stimes :: Integral b => b -> POP f xss -> POP f xss #
Show (NP (NP f) xss) => Show (POP f xss) # |
Instance details Defined in Data.SOP.NP Methods showsPrec :: Int -> POP f xss -> ShowS # show :: POP f xss -> String # showList :: [POP f xss] -> ShowS #
Eq (NP (NP f) xss) => Eq (POP f xss) # |
Instance details Defined in Data.SOP.NP Methods (==) :: POP f xss -> POP f xss -> Bool # (/=) :: POP f xss -> POP f xss -> Bool #
Ord (NP (NP f) xss) => Ord (POP f xss) # |
Instance details Defined in Data.SOP.NP Methods compare :: POP f xss -> POP f xss -> Ordering # (<) :: POP f xss -> POP f xss -> Bool # (<=) :: POP f xss -> POP f xss -> Bool # (>) :: POP f xss -> POP f xss -> Bool # (>=) :: POP f xss -> POP f xss -> Bool # max :: POP f xss -> POP f xss -> POP f xss # min :: POP f xss -> POP f xss -> POP f xss #
type AllZipN (POP :: (k -> Type) -> [[k]] -> Type) (c :: a -> b -> Constraint) # |
Instance details Defined in Data.SOP.NP type AllZipN (POP :: (k -> Type) -> [[k]] -> Type) (c :: a -> b -> Constraint) = AllZip2 c
type Same (POP :: (k1 -> Type) -> [[k1]] -> Type) # |
Instance details Defined in Data.SOP.NP type Same (POP :: (k1 -> Type) -> [[k1]] -> Type) = POP :: (k2 -> Type) -> [[k2]] -> Type
type Prod (POP :: (k -> Type) -> [[k]] -> Type) # |
Instance details Defined in Data.SOP.NP type Prod (POP :: (k -> Type) -> [[k]] -> Type) = POP :: (k -> Type) -> [[k]] -> Type
type UnProd (POP :: (k -> Type) -> [[k]] -> Type) # |
Instance details Defined in Data.SOP.NS type UnProd (POP :: (k -> Type) -> [[k]] -> Type) = SOP :: (k -> Type) -> [[k]] -> Type
type SListIN (POP :: (k -> Type) -> [[k]] -> Type) # |
Instance details Defined in Data.SOP.NP type SListIN (POP :: (k -> Type) -> [[k]] -> Type) = SListI2 :: [[k]] -> Constraint
type CollapseTo (POP :: (k -> Type) -> [[k]] -> Type) a # |
Instance details Defined in Data.SOP.NP type CollapseTo (POP :: (k -> Type) -> [[k]] -> Type) a = [[a]]
type AllN (POP :: (k -> Type) -> [[k]] -> Type) (c :: k -> Constraint) # |
Instance details Defined in Data.SOP.NP type AllN (POP :: (k -> Type) -> [[k]] -> Type) (c :: k -> Constraint) = All2 c

unPOP :: forall {k} (f :: k -> Type) (xss :: [[k]]). POP f xss -> NP (NP f) xss #

Unwrap a product of products.

# Combinators

## Constructing products

class HPure (h :: (k -> Type) -> l -> Type) where #

A generalization of `pure` or `return` to higher kinds.

Methods

hpure :: forall (xs :: l) f. SListIN h xs => (forall (a :: k). f a) -> h f xs #

Corresponds to `pure` directly.

Instances:

    hpure, pure_NP  :: SListI  xs  => (forall a. f a) -> NP  f xs
    hpure, pure_POP :: SListI2 xss => (forall a. f a) -> POP f xss

hcpure :: forall c (xs :: l) proxy f. AllN h c xs => proxy c -> (forall (a :: k). c a => f a) -> h f xs #

A variant of `hpure` that allows passing in a constrained argument.

Calling ``hcpure` f s` where `s :: h f xs` causes `f` to be applied at all the types that are contained in `xs`. Therefore, the constraint `c` has to be satisfied for all elements of `xs`, which is what ``AllN` h c xs` states.

Instances:

    hcpure, cpure_NP  :: (All  c xs ) => proxy c -> (forall a. c a => f a) -> NP  f xs
    hcpure, cpure_POP :: (All2 c xss) => proxy c -> (forall a. c a => f a) -> POP f xss

#### Instances

Instances details

HPure (POP :: (k -> Type) -> [[k]] -> Type) # |
Instance details Defined in Data.SOP.NP Methods hpure :: forall (xs :: [[k]]) f. SListIN (POP :: (k -> Type) -> [[k]] -> Type) xs => (forall (a :: k). f a) -> POP f xs # hcpure :: forall c (xs :: [[k]]) proxy f. AllN (POP :: (k -> Type) -> [[k]] -> Type) c xs => proxy c -> (forall (a :: k). c a => f a) -> POP f xs #
HPure (NP :: (k -> Type) -> [k] -> Type) # |
Instance details Defined in Data.SOP.NP Methods hpure :: forall (xs :: [k]) f. SListIN (NP :: (k -> Type) -> [k] -> Type) xs => (forall (a :: k). f a) -> NP f xs # hcpure :: forall c (xs :: [k]) proxy f. AllN (NP :: (k -> Type) -> [k] -> Type) c xs => proxy c -> (forall (a :: k). c a => f a) -> NP f xs #

## Destructing products

hd :: forall {k} f (x :: k) (xs :: [k]). NP f (x ': xs) -> f x #

Obtain the head of an n-ary product.

Since: 0.2.1.0

tl :: forall {k} (f :: k -> Type) (x :: k) (xs :: [k]). NP f (x ': xs) -> NP f xs #

Obtain the tail of an n-ary product.

Since: 0.2.1.0

type Projection (f :: k -> Type) (xs :: [k]) = (K (NP f xs) :: k -> Type) -.-> f #

The type of projections from an n-ary product.

A projection is a function from the n-ary product to a single element.

projections :: forall {k} (xs :: [k]) (f :: k -> Type). SListI xs => NP (Projection f xs) xs #

Compute all projections from an n-ary product.

Each element of the resulting product contains one of the projections.

shiftProjection :: forall {a1} (f :: a1 -> Type) (xs :: [a1]) (a2 :: a1) (x :: a1). Projection f xs a2 -> Projection f (x ': xs) a2 #

## Application

newtype ((f :: k -> Type) -.-> (g :: k -> Type)) (a :: k) infixr 1 #

Lifted functions.

Constructors

Fn |

Fields

- apFn :: f a -> g a

fn :: forall {k} f (a :: k) f'. (f a -> f' a) -> (f -.-> f') a #

Construct a lifted function.

Same as `Fn`. Only available for uniformity with the higher-arity versions.

fn_2 :: forall {k} f (a :: k) f' f''. (f a -> f' a -> f'' a) -> (f -.-> (f' -.-> f'')) a #

Construct a binary lifted function.

fn_3 :: forall {k} f (a :: k) f' f'' f'''. (f a -> f' a -> f'' a -> f''' a) -> (f -.-> (f' -.-> (f'' -.-> f'''))) a #

Construct a ternary lifted function.

fn_4 :: forall {k} f (a :: k) f' f'' f''' f''''. (f a -> f' a -> f'' a -> f''' a -> f'''' a) -> (f -.-> (f' -.-> (f'' -.-> (f''' -.-> f'''')))) a #

Construct a quarternary lifted function.

type family Prod (h :: (k -> Type) -> l -> Type) :: (k -> Type) -> l -> Type #

Maps a structure containing sums to the corresponding product structure.

#### Instances

Instances details

type Prod (POP :: (k -> Type) -> [[k]] -> Type) # |
Instance details Defined in Data.SOP.NP type Prod (POP :: (k -> Type) -> [[k]] -> Type) = POP :: (k -> Type) -> [[k]] -> Type
type Prod (SOP :: (k -> Type) -> [[k]] -> Type) # |
Instance details Defined in Data.SOP.NS type Prod (SOP :: (k -> Type) -> [[k]] -> Type) = POP :: (k -> Type) -> [[k]] -> Type
type Prod (NP :: (k -> Type) -> [k] -> Type) # |
Instance details Defined in Data.SOP.NP type Prod (NP :: (k -> Type) -> [k] -> Type) = NP :: (k -> Type) -> [k] -> Type
type Prod (NS :: (k -> Type) -> [k] -> Type) # |
Instance details Defined in Data.SOP.NS type Prod (NS :: (k -> Type) -> [k] -> Type) = NP :: (k -> Type) -> [k] -> Type

class (Prod (Prod h) ~ Prod h, HPure (Prod h)) => HAp (h :: (k -> Type) -> l -> Type) where #

A generalization of `<*>`.

Methods

hap :: forall (f :: k -> Type) (g :: k -> Type) (xs :: l). Prod h (f -.-> g) xs -> h f xs -> h g xs #

Corresponds to `<*>`.

For products (`NP`) as well as products of products (`POP`), the correspondence is rather direct. We combine a structure containing (lifted) functions and a compatible structure containing corresponding arguments into a compatible structure containing results.

The same combinator can also be used to combine a product structure of functions with a sum structure of arguments, which then results in another sum structure of results. The sum structure determines which part of the product structure will be used.

Instances:

    hap, ap_NP  :: NP  (f -.-> g) xs  -> NP  f xs  -> NP  g xs
    hap, ap_NS  :: NP  (f -.-> g) xs  -> NS  f xs  -> NS  g xs
    hap, ap_POP :: POP (f -.-> g) xss -> POP f xss -> POP g xss
    hap, ap_SOP :: POP (f -.-> g) xss -> SOP f xss -> SOP g xss

#### Instances

Instances details

HAp (POP :: (k -> Type) -> [[k]] -> Type) # |
Instance details Defined in Data.SOP.NP Methods hap :: forall (f :: k -> Type) (g :: k -> Type) (xs :: [[k]]). Prod (POP :: (k -> Type) -> [[k]] -> Type) (f -.-> g) xs -> POP f xs -> POP g xs #
HAp (SOP :: (k -> Type) -> [[k]] -> Type) # |
Instance details Defined in Data.SOP.NS Methods hap :: forall (f :: k -> Type) (g :: k -> Type) (xs :: [[k]]). Prod (SOP :: (k -> Type) -> [[k]] -> Type) (f -.-> g) xs -> SOP f xs -> SOP g xs #
HAp (NP :: (k -> Type) -> [k] -> Type) # |
Instance details Defined in Data.SOP.NP Methods hap :: forall (f :: k -> Type) (g :: k -> Type) (xs :: [k]). Prod (NP :: (k -> Type) -> [k] -> Type) (f -.-> g) xs -> NP f xs -> NP g xs #
HAp (NS :: (k -> Type) -> [k] -> Type) # |
Instance details Defined in Data.SOP.NS Methods hap :: forall (f :: k -> Type) (g :: k -> Type) (xs :: [k]). Prod (NS :: (k -> Type) -> [k] -> Type) (f -.-> g) xs -> NS f xs -> NS g xs #

## Lifting / mapping

hliftA :: forall {k} {l} h (xs :: l) f f'. (SListIN (Prod h) xs, HAp h) => (forall (a :: k). f a -> f' a) -> h f xs -> h f' xs #

A generalized form of `liftA`, which in turn is a generalized `map`.

Takes a lifted function and applies it to every element of a structure while preserving its shape.

Specification:

    hliftA f xs = hpure (fn f) ` hap ` xs

Instances:

    hliftA, liftA_NP  :: SListI  xs  => (forall a. f a -> f' a) -> NP  f xs  -> NP  f' xs
    hliftA, liftA_NS  :: SListI  xs  => (forall a. f a -> f' a) -> NS  f xs  -> NS  f' xs
    hliftA, liftA_POP :: SListI2 xss => (forall a. f a -> f' a) -> POP f xss -> POP f' xss
    hliftA, liftA_SOP :: SListI2 xss => (forall a. f a -> f' a) -> SOP f xss -> SOP f' xss

hliftA2 :: forall {k} {l} h (xs :: l) f f' f''. (SListIN (Prod h) xs, HAp h, HAp (Prod h)) => (forall (a :: k). f a -> f' a -> f'' a) -> Prod h f xs -> h f' xs -> h f'' xs #

A generalized form of `liftA2`, which in turn is a generalized `zipWith`.

Takes a lifted binary function and uses it to combine two structures of equal shape into a single structure.

It either takes two product structures to a product structure, or one product and one sum structure to a sum structure.

Specification:

    hliftA2 f xs ys = hpure (fn_2 f) ` hap ` xs ` hap ` ys

Instances:

    hliftA2, liftA2_NP  :: SListI  xs  => (forall a. f a -> f' a -> f'' a) -> NP  f xs  -> NP  f' xs  -> NP  f'' xs
    hliftA2, liftA2_NS  :: SListI  xs  => (forall a. f a -> f' a -> f'' a) -> NP  f xs  -> NS  f' xs  -> NS  f'' xs
    hliftA2, liftA2_POP :: SListI2 xss => (forall a. f a -> f' a -> f'' a) -> POP f xss -> POP f' xss -> POP f'' xss
    hliftA2, liftA2_SOP :: SListI2 xss => (forall a. f a -> f' a -> f'' a) -> POP f xss -> SOP f' xss -> SOP f'' xss

hliftA3 :: forall {k} {l} h (xs :: l) f f' f'' f'''. (SListIN (Prod h) xs, HAp h, HAp (Prod h)) => (forall (a :: k). f a -> f' a -> f'' a -> f''' a) -> Prod h f xs -> Prod h f' xs -> h f'' xs -> h f''' xs #

A generalized form of `liftA3`, which in turn is a generalized `zipWith3`.

Takes a lifted ternary function and uses it to combine three structures of equal shape into a single structure.

It either takes three product structures to a product structure, or two product structures and one sum structure to a sum structure.

Specification:

    hliftA3 f xs ys zs = hpure (fn_3 f) ` hap ` xs ` hap ` ys ` hap ` zs

Instances:

    hliftA3, liftA3_NP  :: SListI  xs  => (forall a. f a -> f' a -> f'' a -> f''' a) -> NP  f xs  -> NP  f' xs  -> NP  f'' xs  -> NP  f''' xs
    hliftA3, liftA3_NS  :: SListI  xs  => (forall a. f a -> f' a -> f'' a -> f''' a) -> NP  f xs  -> NP  f' xs  -> NS  f'' xs  -> NS  f''' xs
    hliftA3, liftA3_POP :: SListI2 xss => (forall a. f a -> f' a -> f'' a -> f''' a) -> POP f xss -> POP f' xss -> POP f'' xss -> POP f''' xs
    hliftA3, liftA3_SOP :: SListI2 xss => (forall a. f a -> f' a -> f'' a -> f''' a) -> POP f xss -> POP f' xss -> SOP f'' xss -> SOP f''' xs

hcliftA :: forall {k} {l} h c (xs :: l) proxy f f'. (AllN (Prod h) c xs, HAp h) => proxy c -> (forall (a :: k). c a => f a -> f' a) -> h f xs -> h f' xs #

Variant of `hliftA` that takes a constrained function.

Specification:

    hcliftA p f xs = hcpure p (fn f) ` hap ` xs

hcliftA2 :: forall {k} {l} h c (xs :: l) proxy f f' f''. (AllN (Prod h) c xs, HAp h, HAp (Prod h)) => proxy c -> (forall (a :: k). c a => f a -> f' a -> f'' a) -> Prod h f xs -> h f' xs -> h f'' xs #

Variant of `hliftA2` that takes a constrained function.

Specification:

    hcliftA2 p f xs ys = hcpure p (fn_2 f) ` hap ` xs ` hap ` ys

hcliftA3 :: forall {k} {l} h c (xs :: l) proxy f f' f'' f'''. (AllN (Prod h) c xs, HAp h, HAp (Prod h)) => proxy c -> (forall (a :: k). c a => f a -> f' a -> f'' a -> f''' a) -> Prod h f xs -> Prod h f' xs -> h f'' xs -> h f''' xs #

Variant of `hliftA3` that takes a constrained function.

Specification:

    hcliftA3 p f xs ys zs = hcpure p (fn_3 f) ` hap ` xs ` hap ` ys ` hap ` zs

hmap :: forall {k} {l} h (xs :: l) f f'. (SListIN (Prod h) xs, HAp h) => (forall (a :: k). f a -> f' a) -> h f xs -> h f' xs #

Another name for `hliftA`.

Since: 0.2

hzipWith :: forall {k} {l} h (xs :: l) f f' f''. (SListIN (Prod h) xs, HAp h, HAp (Prod h)) => (forall (a :: k). f a -> f' a -> f'' a) -> Prod h f xs -> h f' xs -> h f'' xs #

Another name for `hliftA2`.

Since: 0.2

hzipWith3 :: forall {k} {l} h (xs :: l) f f' f'' f'''. (SListIN (Prod h) xs, HAp h, HAp (Prod h)) => (forall (a :: k). f a -> f' a -> f'' a -> f''' a) -> Prod h f xs -> Prod h f' xs -> h f'' xs -> h f''' xs #

Another name for `hliftA3`.

Since: 0.2

hcmap :: forall {k} {l} h c (xs :: l) proxy f f'. (AllN (Prod h) c xs, HAp h) => proxy c -> (forall (a :: k). c a => f a -> f' a) -> h f xs -> h f' xs #

Another name for `hcliftA`.

Since: 0.2

hczipWith :: forall {k} {l} h c (xs :: l) proxy f f' f''. (AllN (Prod h) c xs, HAp h, HAp (Prod h)) => proxy c -> (forall (a :: k). c a => f a -> f' a -> f'' a) -> Prod h f xs -> h f' xs -> h f'' xs #

Another name for `hcliftA2`.

Since: 0.2

hczipWith3 :: forall {k} {l} h c (xs :: l) proxy f f' f'' f'''. (AllN (Prod h) c xs, HAp h, HAp (Prod h)) => proxy c -> (forall (a :: k). c a => f a -> f' a -> f'' a -> f''' a) -> Prod h f xs -> Prod h f' xs -> h f'' xs -> h f''' xs #

Another name for `hcliftA3`.

Since: 0.2

## Constructing sums

type Injection (f :: k -> Type) (xs :: [k]) = f -.-> (K (NS f xs) :: k -> Type) #

The type of injections into an n-ary sum.

If you expand the type synonyms and newtypes involved, you get

    Injection f xs a = (f -.-> K (NS f xs)) a ~= f a -> K (NS f xs) a ~= f a -> NS f xs

If we pick `a` to be an element of `xs`, this indeed corresponds to an injection into the sum.

injections :: forall {k} (xs :: [k]) (f :: k -> Type). SListI xs => NP (Injection f xs) xs #

Compute all injections into an n-ary sum.

Each element of the resulting product contains one of the injections.

shift :: forall {a1} (f :: a1 -> Type) (xs :: [a1]) (a2 :: a1) (x :: a1). Injection f xs a2 -> Injection f (x ': xs) a2 #

Deprecated: Use `shiftInjection` instead.

Shift an injection.

Given an injection, return an injection into a sum that is one component larger.

shiftInjection :: forall {a1} (f :: a1 -> Type) (xs :: [a1]) (a2 :: a1) (x :: a1). Injection f xs a2 -> Injection f (x ': xs) a2 #

Shift an injection.

Given an injection, return an injection into a sum that is one component larger.

type family UnProd (h :: (k -> Type) -> l -> Type) :: (k -> Type) -> l -> Type #

Maps a structure containing products to the corresponding sum structure.

Since: 0.2.4.0

#### Instances

Instances details

type UnProd (POP :: (k -> Type) -> [[k]] -> Type) # |
Instance details Defined in Data.SOP.NS type UnProd (POP :: (k -> Type) -> [[k]] -> Type) = SOP :: (k -> Type) -> [[k]] -> Type
type UnProd (NP :: (k -> Type) -> [k] -> Type) # |
Instance details Defined in Data.SOP.NS type UnProd (NP :: (k -> Type) -> [k] -> Type) = NS :: (k -> Type) -> [k] -> Type

class UnProd (Prod h) ~ h => HApInjs (h :: (k -> Type) -> l -> Type) where #

A class for applying all injections corresponding to a sum-like structure to a table containing suitable arguments.

Methods

hapInjs :: forall (xs :: l) (f :: k -> Type). SListIN h xs => Prod h f xs -> [h f xs] #

For a given table (product-like structure), produce a list where each element corresponds to the application of an injection function into the corresponding sum-like structure.

Instances:

    hapInjs, apInjs_NP  :: SListI  xs  => NP  f xs -> [NS  f xs ]
    hapInjs, apInjs_SOP :: SListI2 xss => POP f xs -> [SOP f xss]

Examples:

    >>> hapInjs (I 'x' :* I True :* I 2 :* Nil) :: [NS I '[Char, Bool, Int]]
    [Z (I 'x'),S (Z (I True)),S (S (Z (I 2)))]

    >>> hapInjs (POP ((I 'x' :* Nil) :* (I True :* I 2 :* Nil) :* Nil)) :: [SOP I '[ '[Char], '[Bool, Int]]]
    [SOP (Z (I 'x' :* Nil)),SOP (S (Z (I True :* I 2 :* Nil)))]

Unfortunately the type-signatures are required in GHC-7.10 and older.

Since: 0.2.4.0

#### Instances

Instances details

HApInjs (SOP :: (k -> Type) -> [[k]] -> Type) # |
Instance details Defined in Data.SOP.NS Methods hapInjs :: forall (xs :: [[k]]) (f :: k -> Type). SListIN (SOP :: (k -> Type) -> [[k]] -> Type) xs => Prod (SOP :: (k -> Type) -> [[k]] -> Type) f xs -> [SOP f xs] #
HApInjs (NS :: (k -> Type) -> [k] -> Type) # |
Instance details Defined in Data.SOP.NS Methods hapInjs :: forall (xs :: [k]) (f :: k -> Type). SListIN (NS :: (k -> Type) -> [k] -> Type) xs => Prod (NS :: (k -> Type) -> [k] -> Type) f xs -> [NS f xs] #

apInjs_NP :: forall {k} (xs :: [k]) (f :: k -> Type). SListI xs => NP f xs -> [NS f xs] #

Apply injections to a product.

Given a product containing all possible choices, produce a list of sums by applying each injection to the appropriate element.

Example:

    >>> apInjs_NP (I 'x' :* I True :* I 2 :* Nil)
    [Z (I 'x'),S (Z (I True)),S (S (Z (I 2)))]

apInjs_POP :: forall {k} (xss :: [[k]]) (f :: k -> Type). SListI xss => POP f xss -> [SOP f xss] #

Apply injections to a product of product.

This operates on the outer product only. Given a product containing all possible choices (that are products), produce a list of sums (of products) by applying each injection to the appropriate element.

Example:

    >>> apInjs_POP (POP ((I 'x' :* Nil) :* (I True :* I 2 :* Nil) :* Nil))
    [SOP (Z (I 'x' :* Nil)),SOP (S (Z (I True :* I 2 :* Nil)))]

## Destructing sums

unZ :: forall {k} f (x :: k). NS f '[x] -> f x #

Extract the payload from a unary sum.

For larger sums, this function would be partial, so it is only provided with a rather restrictive type.

Example:

    >>> unZ (Z (I 'x'))
    I 'x'

Since: 0.2.2.0

class HIndex (h :: (k -> Type) -> l -> Type) where #

A class for determining which choice in a sum-like structure a value represents.

Methods

hindex :: forall (f :: k -> Type) (xs :: l). h f xs -> Int #

If `h` is a sum-like structure representing a choice between `n` different options, and `x` is a value of type `h f xs`, then ``hindex` x` returns a number between `0` and `n - 1` representing the index of the choice made by `x`.

Instances:

    hindex, index_NS  :: NS  f xs -> Int
    hindex, index_SOP :: SOP f xs -> Int

Examples:

    >>> hindex (S (S (Z (I False))))
    2
    >>> hindex (Z (K ()))
    0
    >>> hindex (SOP (S (Z (I True :* I 'x' :* Nil))))
    1

Since: 0.2.4.0

#### Instances

Instances details

HIndex (SOP :: (k -> Type) -> [[k]] -> Type) # |
Instance details Defined in Data.SOP.NS Methods hindex :: forall (f :: k -> Type) (xs :: [[k]]). SOP f xs -> Int #
HIndex (NS :: (k -> Type) -> [k] -> Type) # |
Instance details Defined in Data.SOP.NS Methods hindex :: forall (f :: k -> Type) (xs :: [k]). NS f xs -> Int #

## Dealing with ``All` c`

hcliftA' :: forall {k} (c :: k -> Constraint) (xss :: [[k]]) h proxy f f'. (All2 c xss, Prod h ~ (NP :: ([k] -> Type) -> [[k]] -> Type), HAp h) => proxy c -> (forall (xs :: [k]). All c xs => f xs -> f' xs) -> h f xss -> h f' xss #

Deprecated: Use `hcliftA` or `hcmap` instead.

Lift a constrained function operating on a list-indexed structure to a function on a list-of-list-indexed structure.

This is a variant of `hcliftA`.

Specification:

    hcliftA' p f xs = hpure (fn_2 $ \ AllDictC -> f) ` hap ` allDict_NP p ` hap ` xs

Instances:

    hcliftA' :: All2 c xss => proxy c -> (forall xs. All c xs => f xs -> f' xs) -> NP f xss -> NP f' xss
    hcliftA' :: All2 c xss => proxy c -> (forall xs. All c xs => f xs -> f' xs) -> NS f xss -> NS f' xss

hcliftA2' :: forall {k} (c :: k -> Constraint) (xss :: [[k]]) h proxy f f' f''. (All2 c xss, Prod h ~ (NP :: ([k] -> Type) -> [[k]] -> Type), HAp h) => proxy c -> (forall (xs :: [k]). All c xs => f xs -> f' xs -> f'' xs) -> Prod h f xss -> h f' xss -> h f'' xss #

Deprecated: Use `hcliftA2` or `hczipWith` instead.

Like `hcliftA'`, but for binary functions.

hcliftA3' :: forall {k} (c :: k -> Constraint) (xss :: [[k]]) h proxy f f' f'' f'''. (All2 c xss, Prod h ~ (NP :: ([k] -> Type) -> [[k]] -> Type), HAp h) => proxy c -> (forall (xs :: [k]). All c xs => f xs -> f' xs -> f'' xs -> f''' xs) -> Prod h f xss -> Prod h f' xss -> h f'' xss -> h f''' xss #

Deprecated: Use `hcliftA3` or `hczipWith3` instead.

Like `hcliftA'`, but for ternary functions.

## Comparison

compare_NS #

Arguments

:: forall {k} r f g (xs :: [k]). r | what to do if first is smaller
-> (forall (x :: k). f x -> g x -> r) | what to do if both are equal
-> r | what to do if first is larger
-> NS f xs |
-> NS g xs |
-> r |

Compare two sums with respect to the choice they are making.

A value that chooses the first option is considered smaller than one that chooses the second option.

If the choices are different, then either the first (if the first is smaller than the second) or the third (if the first is larger than the second) argument are called. If both choices are equal, then the second argument is called, which has access to the elements contained in the sums.

Since: 0.3.2.0

ccompare_NS #

Arguments

:: forall {k} c proxy r f g (xs :: [k]). All c xs |
=> proxy c |
-> r | what to do if first is smaller
-> (forall (x :: k). c x => f x -> g x -> r) | what to do if both are equal
-> r | what to do if first is larger
-> NS f xs |
-> NS g xs |
-> r |

Constrained version of `compare_NS`.

Since: 0.3.2.0

compare_SOP #

Arguments

:: forall {k} r (f :: k -> Type) (g :: k -> Type) (xss :: [[k]]). r | what to do if first is smaller
-> (forall (xs :: [k]). NP f xs -> NP g xs -> r) | what to do if both are equal
-> r | what to do if first is larger
-> SOP f xss |
-> SOP g xss |
-> r |

Compare two sums of products with respect to the choice in the sum they are making.

Only the sum structure is used for comparison. This is a small wrapper around `ccompare_NS` for a common special case.

Since: 0.3.2.0

ccompare_SOP #

Arguments

:: forall {k} (c :: k -> Constraint) proxy r (f :: k -> Type) (g :: k -> Type) (xss :: [[k]]). All2 c xss |
=> proxy c |
-> r | what to do if first is smaller
-> (forall (xs :: [k]). All c xs => NP f xs -> NP g xs -> r) | what to do if both are equal
-> r | what to do if first is larger
-> SOP f xss |
-> SOP g xss |
-> r |

Constrained version of `compare_SOP`.

Since: 0.3.2.0

## Collapsing

type family CollapseTo (h :: (k -> Type) -> l -> Type) x #

Maps products to lists, and sums to identities.

#### Instances

Instances details

type CollapseTo (POP :: (k -> Type) -> [[k]] -> Type) a # |
Instance details Defined in Data.SOP.NP type CollapseTo (POP :: (k -> Type) -> [[k]] -> Type) a = [[a]]
type CollapseTo (SOP :: (k -> Type) -> [[k]] -> Type) a # |
Instance details Defined in Data.SOP.NS type CollapseTo (SOP :: (k -> Type) -> [[k]] -> Type) a = [a]
type CollapseTo (NP :: (k -> Type) -> [k] -> Type) a # |
Instance details Defined in Data.SOP.NP type CollapseTo (NP :: (k -> Type) -> [k] -> Type) a = [a]
type CollapseTo (NS :: (k -> Type) -> [k] -> Type) a # |
Instance details Defined in Data.SOP.NS type CollapseTo (NS :: (k -> Type) -> [k] -> Type) a = a

class HCollapse (h :: (k -> Type) -> l -> Type) where #

A class for collapsing a heterogeneous structure into a homogeneous one.

Methods

hcollapse :: forall (xs :: l) a. SListIN h xs => h (K a :: k -> Type) xs -> CollapseTo h a #

Collapse a heterogeneous structure with homogeneous elements into a homogeneous structure.

If a heterogeneous structure is instantiated to the constant functor `K`, then it is in fact homogeneous. This function maps such a value to a simpler Haskell datatype reflecting that. An ``NS` (`K` a)` contains a single `a`, and an ``NP` (`K` a)` contains a list of `a`s.

Instances:

    hcollapse, collapse_NP  :: NP  (K a) xs  ->  [a]
    hcollapse, collapse_NS  :: NS  (K a) xs  ->   a
    hcollapse, collapse_POP :: POP (K a) xss -> [[a]]
    hcollapse, collapse_SOP :: SOP (K a) xss ->  [a]

#### Instances

Instances details

HCollapse (POP :: (k -> Type) -> [[k]] -> Type) # |
Instance details Defined in Data.SOP.NP Methods hcollapse :: forall (xs :: [[k]]) a. SListIN (POP :: (k -> Type) -> [[k]] -> Type) xs => POP (K a :: k -> Type) xs -> CollapseTo (POP :: (k -> Type) -> [[k]] -> Type) a #
HCollapse (SOP :: (k -> Type) -> [[k]] -> Type) # |
Instance details Defined in Data.SOP.NS Methods hcollapse :: forall (xs :: [[k]]) a. SListIN (SOP :: (k -> Type) -> [[k]] -> Type) xs => SOP (K a :: k -> Type) xs -> CollapseTo (SOP :: (k -> Type) -> [[k]] -> Type) a #
HCollapse (NP :: (k -> Type) -> [k] -> Type) # |
Instance details Defined in Data.SOP.NP Methods hcollapse :: forall (xs :: [k]) a. SListIN (NP :: (k -> Type) -> [k] -> Type) xs => NP (K a :: k -> Type) xs -> CollapseTo (NP :: (k -> Type) -> [k] -> Type) a #
HCollapse (NS :: (k -> Type) -> [k] -> Type) # |
Instance details Defined in Data.SOP.NS Methods hcollapse :: forall (xs :: [k]) a. SListIN (NS :: (k -> Type) -> [k] -> Type) xs => NS (K a :: k -> Type) xs -> CollapseTo (NS :: (k -> Type) -> [k] -> Type) a #

## Folding and sequencing

class HTraverse_ (h :: (k -> Type) -> l -> Type) where #

A generalization of `traverse_` or `foldMap`.

Since: 0.3.2.0

Methods

hctraverse_ :: forall c (xs :: l) g proxy f. (AllN h c xs, Applicative g) => proxy c -> (forall (a :: k). c a => f a -> g ()) -> h f xs -> g () #

Corresponds to `traverse_`.

Instances:

    hctraverse_, ctraverse__NP  :: (All  c xs , Applicative g) => proxy c -> (forall a. c a => f a -> g ()) -> NP  f xs  -> g ()
    hctraverse_, ctraverse__NS  :: (All2 c xs , Applicative g) => proxy c -> (forall a. c a => f a -> g ()) -> NS  f xs  -> g ()
    hctraverse_, ctraverse__POP :: (All  c xss, Applicative g) => proxy c -> (forall a. c a => f a -> g ()) -> POP f xss -> g ()
    hctraverse_, ctraverse__SOP :: (All2 c xss, Applicative g) => proxy c -> (forall a. c a => f a -> g ()) -> SOP f xss -> g ()

Since: 0.3.2.0

htraverse_ :: forall (xs :: l) g f. (SListIN h xs, Applicative g) => (forall (a :: k). f a -> g ()) -> h f xs -> g () #

Unconstrained version of `hctraverse_`.

Instances:

    traverse_, traverse__NP  :: (SListI  xs , Applicative g) => (forall a. f a -> g ()) -> NP  f xs  -> g ()
    traverse_, traverse__NS  :: (SListI  xs , Applicative g) => (forall a. f a -> g ()) -> NS  f xs  -> g ()
    traverse_, traverse__POP :: (SListI2 xss, Applicative g) => (forall a. f a -> g ()) -> POP f xss -> g ()
    traverse_, traverse__SOP :: (SListI2 xss, Applicative g) => (forall a. f a -> g ()) -> SOP f xss -> g ()

Since: 0.3.2.0

#### Instances

Instances details

HTraverse_ (POP :: (k -> Type) -> [[k]] -> Type) # |
Instance details Defined in Data.SOP.NP Methods hctraverse_ :: forall c (xs :: [[k]]) g proxy f. (AllN (POP :: (k -> Type) -> [[k]] -> Type) c xs, Applicative g) => proxy c -> (forall (a :: k). c a => f a -> g ()) -> POP f xs -> g () # htraverse_ :: forall (xs :: [[k]]) g f. (SListIN (POP :: (k -> Type) -> [[k]] -> Type) xs, Applicative g) => (forall (a :: k). f a -> g ()) -> POP f xs -> g () #
HTraverse_ (SOP :: (k -> Type) -> [[k]] -> Type) # |
Instance details Defined in Data.SOP.NS Methods hctraverse_ :: forall c (xs :: [[k]]) g proxy f. (AllN (SOP :: (k -> Type) -> [[k]] -> Type) c xs, Applicative g) => proxy c -> (forall (a :: k). c a => f a -> g ()) -> SOP f xs -> g () # htraverse_ :: forall (xs :: [[k]]) g f. (SListIN (SOP :: (k -> Type) -> [[k]] -> Type) xs, Applicative g) => (forall (a :: k). f a -> g ()) -> SOP f xs -> g () #
HTraverse_ (NP :: (k -> Type) -> [k] -> Type) # |
Instance details Defined in Data.SOP.NP Methods hctraverse_ :: forall c (xs :: [k]) g proxy f. (AllN (NP :: (k -> Type) -> [k] -> Type) c xs, Applicative g) => proxy c -> (forall (a :: k). c a => f a -> g ()) -> NP f xs -> g () # htraverse_ :: forall (xs :: [k]) g f. (SListIN (NP :: (k -> Type) -> [k] -> Type) xs, Applicative g) => (forall (a :: k). f a -> g ()) -> NP f xs -> g () #
HTraverse_ (NS :: (k -> Type) -> [k] -> Type) # |
Instance details Defined in Data.SOP.NS Methods hctraverse_ :: forall c (xs :: [k]) g proxy f. (AllN (NS :: (k -> Type) -> [k] -> Type) c xs, Applicative g) => proxy c -> (forall (a :: k). c a => f a -> g ()) -> NS f xs -> g () # htraverse_ :: forall (xs :: [k]) g f. (SListIN (NS :: (k -> Type) -> [k] -> Type) xs, Applicative g) => (forall (a :: k). f a -> g ()) -> NS f xs -> g () #

hcfoldMap :: forall {k} {l} h c (xs :: l) m proxy f. (HTraverse_ h, AllN h c xs, Monoid m) => proxy c -> (forall (a :: k). c a => f a -> m) -> h f xs -> m #

Special case of `hctraverse_`.

Since: 0.3.2.0

hcfor_ :: forall {k} {l} h c (xs :: l) g proxy f. (HTraverse_ h, AllN h c xs, Applicative g) => proxy c -> h f xs -> (forall (a :: k). c a => f a -> g ()) -> g () #

Flipped version of `hctraverse_`.

Since: 0.3.2.0

class HAp h => HSequence (h :: (k -> Type) -> l -> Type) where #

A generalization of `sequenceA`.

Methods

hsequence' :: forall (xs :: l) f (g :: k -> Type). (SListIN h xs, Applicative f) => h (f :.: g) xs -> f (h g xs) #

Corresponds to `sequenceA`.

Lifts an applicative functor out of a structure.

Instances:

    hsequence', sequence'_NP  :: (SListI  xs , Applicative f) => NP  (f :.: g) xs  -> f (NP  g xs )
    hsequence', sequence'_NS  :: (SListI  xs , Applicative f) => NS  (f :.: g) xs  -> f (NS  g xs )
    hsequence', sequence'_POP :: (SListI2 xss, Applicative f) => POP (f :.: g) xss -> f (POP g xss)
    hsequence', sequence'_SOP :: (SListI2 xss, Applicative f) => SOP (f :.: g) xss -> f (SOP g xss)

hctraverse' :: forall c (xs :: l) g proxy f f'. (AllN h c xs, Applicative g) => proxy c -> (forall (a :: k). c a => f a -> g (f' a)) -> h f xs -> g (h f' xs) #

Corresponds to `traverse`.

Instances:

    hctraverse', ctraverse'_NP  :: (All  c xs , Applicative g) => proxy c -> (forall a. c a => f a -> g (f' a)) -> NP  f xs  -> g (NP  f' xs )
    hctraverse', ctraverse'_NS  :: (All2 c xs , Applicative g) => proxy c -> (forall a. c a => f a -> g (f' a)) -> NS  f xs  -> g (NS  f' xs )
    hctraverse', ctraverse'_POP :: (All  c xss, Applicative g) => proxy c -> (forall a. c a => f a -> g (f' a)) -> POP f xss -> g (POP f' xss)
    hctraverse', ctraverse'_SOP :: (All2 c xss, Applicative g) => proxy c -> (forall a. c a => f a -> g (f' a)) -> SOP f xss -> g (SOP f' xss)

Since: 0.3.2.0

htraverse' :: forall (xs :: l) g f f'. (SListIN h xs, Applicative g) => (forall (a :: k). f a -> g (f' a)) -> h f xs -> g (h f' xs) #

Unconstrained variant of `hctraverse'`.

Instances:

    htraverse', traverse'_NP  :: (SListI  xs , Applicative g) => (forall a. c a => f a -> g (f' a)) -> NP  f xs  -> g (NP  f' xs )
    htraverse', traverse'_NS  :: (SListI2 xs , Applicative g) => (forall a. c a => f a -> g (f' a)) -> NS  f xs  -> g (NS  f' xs )
    htraverse', traverse'_POP :: (SListI  xss, Applicative g) => (forall a. c a => f a -> g (f' a)) -> POP f xss -> g (POP f' xss)
    htraverse', traverse'_SOP :: (SListI2 xss, Applicative g) => (forall a. c a => f a -> g (f' a)) -> SOP f xss -> g (SOP f' xss)

Since: 0.3.2.0

#### Instances

Instances details

HSequence (POP :: (k -> Type) -> [[k]] -> Type) # |

Instance details

Defined in Data.SOP.NP

Methods

hsequence' :: forall (xs :: [[k]]) f (g :: k -> Type). (SListIN (POP :: (k -> Type) -> [[k]] -> Type) xs, Applicative f) => POP (f :.: g) xs -> f (POP g xs) #

hctraverse' :: forall c (xs :: [[k]]) g proxy f f'. (AllN (POP :: (k -> Type) -> [[k]] -> Type) c xs, Applicative g) => proxy c -> (forall (a :: k). c a => f a -> g (f' a)) -> POP f xs -> g (POP f' xs) #

htraverse' :: forall (xs :: [[k]]) g f f'. (SListIN (POP :: (k -> Type) -> [[k]] -> Type) xs, Applicative g) => (forall (a :: k). f a -> g (f' a)) -> POP f xs -> g (POP f' xs) #

HSequence (SOP :: (k -> Type) -> [[k]] -> Type) # |

Instance details

Defined in Data.SOP.NS

Methods

hsequence' :: forall (xs :: [[k]]) f (g :: k -> Type). (SListIN (SOP :: (k -> Type) -> [[k]] -> Type) xs, Applicative f) => SOP (f :.: g) xs -> f (SOP g xs) #

hctraverse' :: forall c (xs :: [[k]]) g proxy f f'. (AllN (SOP :: (k -> Type) -> [[k]] -> Type) c xs, Applicative g) => proxy c -> (forall (a :: k). c a => f a -> g (f' a)) -> SOP f xs -> g (SOP f' xs) #

htraverse' :: forall (xs :: [[k]]) g f f'. (SListIN (SOP :: (k -> Type) -> [[k]] -> Type) xs, Applicative g) => (forall (a :: k). f a -> g (f' a)) -> SOP f xs -> g (SOP f' xs) #

HSequence (NP :: (k -> Type) -> [k] -> Type) # |

Instance details

Defined in Data.SOP.NP

Methods

hsequence' :: forall (xs :: [k]) f (g :: k -> Type). (SListIN (NP :: (k -> Type) -> [k] -> Type) xs, Applicative f) => NP (f :.: g) xs -> f (NP g xs) #

hctraverse' :: forall c (xs :: [k]) g proxy f f'. (AllN (NP :: (k -> Type) -> [k] -> Type) c xs, Applicative g) => proxy c -> (forall (a :: k). c a => f a -> g (f' a)) -> NP f xs -> g (NP f' xs) #

htraverse' :: forall (xs :: [k]) g f f'. (SListIN (NP :: (k -> Type) -> [k] -> Type) xs, Applicative g) => (forall (a :: k). f a -> g (f' a)) -> NP f xs -> g (NP f' xs) #

HSequence (NS :: (k -> Type) -> [k] -> Type) # |

Instance details

Defined in Data.SOP.NS

Methods

hsequence' :: forall (xs :: [k]) f (g :: k -> Type). (SListIN (NS :: (k -> Type) -> [k] -> Type) xs, Applicative f) => NS (f :.: g) xs -> f (NS g xs) #

hctraverse' :: forall c (xs :: [k]) g proxy f f'. (AllN (NS :: (k -> Type) -> [k] -> Type) c xs, Applicative g) => proxy c -> (forall (a :: k). c a => f a -> g (f' a)) -> NS f xs -> g (NS f' xs) #

htraverse' :: forall (xs :: [k]) g f f'. (SListIN (NS :: (k -> Type) -> [k] -> Type) xs, Applicative g) => (forall (a :: k). f a -> g (f' a)) -> NS f xs -> g (NS f' xs) #

hsequence :: forall {l} h (xs :: l) f. (SListIN h xs, SListIN (Prod h) xs, HSequence h, Applicative f) => h f xs -> f (h I xs) #

Special case of `hsequence'` where `g = `I``.

hsequenceK :: forall {k} {l} h (xs :: l) f a. (SListIN h xs, SListIN (Prod h) xs, Applicative f, HSequence h) => h (K (f a) :: k -> Type) xs -> f (h (K a :: k -> Type) xs) #

Special case of `hsequence'` where `g = `K` a`.

hctraverse :: forall {l} h c (xs :: l) g proxy f. (HSequence h, AllN h c xs, Applicative g) => proxy c -> (forall a. c a => f a -> g a) -> h f xs -> g (h I xs) #

Special case of `hctraverse'` where `f' = `I``.

Since: 0.3.2.0

hcfor :: forall {l} h c (xs :: l) g proxy f. (HSequence h, AllN h c xs, Applicative g) => proxy c -> h f xs -> (forall a. c a => f a -> g a) -> g (h I xs) #

Flipped version of `hctraverse`.

Since: 0.3.2.0

## Expanding sums to products

class HExpand (h :: (k -> Type) -> l -> Type) where #

A class for expanding sum structures into corresponding product structures, filling in the slots not targeted by the sum with default values.

Since: 0.2.5.0

Methods

hexpand :: forall (xs :: l) f. SListIN (Prod h) xs => (forall (x :: k). f x) -> h f xs -> Prod h f xs #

Expand a given sum structure into a corresponding product structure by placing the value contained in the sum into the corresponding position in the product, and using the given default value for all other positions.

Instances:

    hexpand, expand_NS  :: SListI xs   => (forall x . f x) -> NS  f xs  -> NP  f xs
    hexpand, expand_SOP :: SListI2 xss => (forall x . f x) -> SOP f xss -> POP f xss

Examples:

    >>> hexpand Nothing (S (Z (Just 3))) :: NP Maybe '[Char, Int, Bool]
    Nothing :* Just 3 :* Nothing :* Nil
    >>> hexpand [] (SOP (S (Z ([1,2] :* "xyz" :* Nil)))) :: POP [] '[ '[Bool], '[Int, Char] ]
    POP (([] :* Nil) :* ([1,2] :* "xyz" :* Nil) :* Nil)

Since: 0.2.5.0

hcexpand :: forall c (xs :: l) proxy f. AllN (Prod h) c xs => proxy c -> (forall (x :: k). c x => f x) -> h f xs -> Prod h f xs #

Variant of `hexpand` that allows passing a constrained default.

Instances:

    hcexpand, cexpand_NS  :: All  c xs  => proxy c -> (forall x . c x => f x) -> NS  f xs  -> NP  f xs
    hcexpand, cexpand_SOP :: All2 c xss => proxy c -> (forall x . c x => f x) -> SOP f xss -> POP f xss

Examples:

    >>> hcexpand (Proxy :: Proxy Bounded) (I minBound) (S (Z (I 20))) :: NP I '[Bool, Int, Ordering]
    I False :* I 20 :* I LT :* Nil
    >>> hcexpand (Proxy :: Proxy Num) (I 0) (SOP (S (Z (I 1 :* I 2 :* Nil)))) :: POP I '[ '[Double], '[Int, Int] ]
    POP ((I 0.0 :* Nil) :* (I 1 :* I 2 :* Nil) :* Nil)

Since: 0.2.5.0

#### Instances

Instances details

HExpand (SOP :: (k -> Type) -> [[k]] -> Type) # |

Instance details

Defined in Data.SOP.NS

Methods

hexpand :: forall (xs :: [[k]]) f. SListIN (Prod (SOP :: (k -> Type) -> [[k]] -> Type)) xs => (forall (x :: k). f x) -> SOP f xs -> Prod (SOP :: (k -> Type) -> [[k]] -> Type) f xs #

hcexpand :: forall c (xs :: [[k]]) proxy f. AllN (Prod (SOP :: (k -> Type) -> [[k]] -> Type)) c xs => proxy c -> (forall (x :: k). c x => f x) -> SOP f xs -> Prod (SOP :: (k -> Type) -> [[k]] -> Type) f xs #

HExpand (NS :: (k -> Type) -> [k] -> Type) # |

Instance details

Defined in Data.SOP.NS

Methods

hexpand :: forall (xs :: [k]) f. SListIN (Prod (NS :: (k -> Type) -> [k] -> Type)) xs => (forall (x :: k). f x) -> NS f xs -> Prod (NS :: (k -> Type) -> [k] -> Type) f xs #

hcexpand :: forall c (xs :: [k]) proxy f. AllN (Prod (NS :: (k -> Type) -> [k] -> Type)) c xs => proxy c -> (forall (x :: k). c x => f x) -> NS f xs -> Prod (NS :: (k -> Type) -> [k] -> Type) f xs #

## Transformation of index lists and coercions

class ((Same h1 :: (k2 -> Type) -> l2 -> Type) ~ h2, (Same h2 :: (k1 -> Type) -> l1 -> Type) ~ h1) => HTrans (h1 :: (k1 -> Type) -> l1 -> Type) (h2 :: (k2 -> Type) -> l2 -> Type) where #

A class for transforming structures into related structures with a different index list, as long as the index lists have the same shape and the elements and interpretation functions are suitably related.

Since: 0.3.1.0

Methods

htrans :: forall c (xs :: l1) (ys :: l2) proxy f g. AllZipN (Prod h1) c xs ys => proxy c -> (forall (x :: k1) (y :: k2). c x y => f x -> g y) -> h1 f xs -> h2 g ys #

Transform a structure into a related structure given a conversion function for the elements.

Since: 0.3.1.0

hcoerce :: forall (f :: k1 -> Type) (g :: k2 -> Type) (xs :: l1) (ys :: l2). AllZipN (Prod h1) (LiftedCoercible f g) xs ys => h1 f xs -> h2 g ys #

Safely coerce a structure into a representationally equal structure.

This is a special case of `htrans`, but can be implemented more efficiently; for example in terms of `unsafeCoerce`.

Examples:

    >>> hcoerce (I (Just LT) :* I (Just 'x') :* I (Just True) :* Nil) :: NP Maybe '[Ordering, Char, Bool]
    Just LT :* Just 'x' :* Just True :* Nil
    >>> hcoerce (SOP (Z (K True :* K False :* Nil))) :: SOP I '[ '[Bool, Bool], '[Bool] ]
    SOP (Z (I True :* I False :* Nil))

Since: 0.3.1.0

#### Instances

Instances details

HTrans (POP :: (k1 -> Type) -> [[k1]] -> Type) (POP :: (k2 -> Type) -> [[k2]] -> Type) # |

Instance details

Defined in Data.SOP.NP

Methods

htrans :: forall c (xs :: [[k1]]) (ys :: [[k2]]) proxy f g. AllZipN (Prod (POP :: (k1 -> Type) -> [[k1]] -> Type)) c xs ys => proxy c -> (forall (x :: k1) (y :: k2). c x y => f x -> g y) -> POP f xs -> POP g ys #

hcoerce :: forall (f :: k1 -> Type) (g :: k2 -> Type) (xs :: [[k1]]) (ys :: [[k2]]). AllZipN (Prod (POP :: (k1 -> Type) -> [[k1]] -> Type)) (LiftedCoercible f g) xs ys => POP f xs -> POP g ys #

HTrans (SOP :: (k1 -> Type) -> [[k1]] -> Type) (SOP :: (k2 -> Type) -> [[k2]] -> Type) # |

Instance details

Defined in Data.SOP.NS

Methods

htrans :: forall c (xs :: [[k1]]) (ys :: [[k2]]) proxy f g. AllZipN (Prod (SOP :: (k1 -> Type) -> [[k1]] -> Type)) c xs ys => proxy c -> (forall (x :: k1) (y :: k2). c x y => f x -> g y) -> SOP f xs -> SOP g ys #

hcoerce :: forall (f :: k1 -> Type) (g :: k2 -> Type) (xs :: [[k1]]) (ys :: [[k2]]). AllZipN (Prod (SOP :: (k1 -> Type) -> [[k1]] -> Type)) (LiftedCoercible f g) xs ys => SOP f xs -> SOP g ys #

HTrans (NP :: (k1 -> Type) -> [k1] -> Type) (NP :: (k2 -> Type) -> [k2] -> Type) # |

Instance details

Defined in Data.SOP.NP

Methods

htrans :: forall c (xs :: [k1]) (ys :: [k2]) proxy f g. AllZipN (Prod (NP :: (k1 -> Type) -> [k1] -> Type)) c xs ys => proxy c -> (forall (x :: k1) (y :: k2). c x y => f x -> g y) -> NP f xs -> NP g ys #

hcoerce :: forall (f :: k1 -> Type) (g :: k2 -> Type) (xs :: [k1]) (ys :: [k2]). AllZipN (Prod (NP :: (k1 -> Type) -> [k1] -> Type)) (LiftedCoercible f g) xs ys => NP f xs -> NP g ys #

HTrans (NS :: (k1 -> Type) -> [k1] -> Type) (NS :: (k2 -> Type) -> [k2] -> Type) # |

Instance details

Defined in Data.SOP.NS

Methods

htrans :: forall c (xs :: [k1]) (ys :: [k2]) proxy f g. AllZipN (Prod (NS :: (k1 -> Type) -> [k1] -> Type)) c xs ys => proxy c -> (forall (x :: k1) (y :: k2). c x y => f x -> g y) -> NS f xs -> NS g ys #

hcoerce :: forall (f :: k1 -> Type) (g :: k2 -> Type) (xs :: [k1]) (ys :: [k2]). AllZipN (Prod (NS :: (k1 -> Type) -> [k1] -> Type)) (LiftedCoercible f g) xs ys => NS f xs -> NS g ys #

hfromI :: forall {l1} {k2} {l2} h1 (f :: k2 -> Type) (xs :: l1) (ys :: l2) h2. (AllZipN (Prod h1) (LiftedCoercible I f) xs ys, HTrans h1 h2) => h1 I xs -> h2 f ys #

Specialization of `hcoerce`.

Since: 0.3.1.0

htoI :: forall {k1} {l1} {l2} h1 (f :: k1 -> Type) (xs :: l1) (ys :: l2) h2. (AllZipN (Prod h1) (LiftedCoercible f I) xs ys, HTrans h1 h2) => h1 f xs -> h2 I ys #

Specialization of `hcoerce`.

Since: 0.3.1.0

## Partial operations

fromList :: forall {k} (xs :: [k]) a. SListI xs => [a] -> Maybe (NP (K a :: k -> Type) xs) #

Construct a homogeneous n-ary product from a normal Haskell list.

Returns `Nothing` if the length of the list does not exactly match the expected size of the product.

# Utilities

## Basic functors

newtype K a (b :: k) #

The constant type functor.

Like `Constant`, but kind-polymorphic in its second argument and with a shorter name.

Constructors

K a |

#### Instances

Instances details

Eq2 (K :: Type -> Type -> Type) # | Since: 0.2.4.0
Instance details Defined in Data.SOP.BasicFunctors Methods liftEq2 :: (a -> b -> Bool) -> (c -> d -> Bool) -> K a c -> K b d -> Bool #
Ord2 (K :: Type -> Type -> Type) # | Since: 0.2.4.0
Instance details Defined in Data.SOP.BasicFunctors Methods liftCompare2 :: (a -> b -> Ordering) -> (c -> d -> Ordering) -> K a c -> K b d -> Ordering #
Read2 (K :: Type -> Type -> Type) # | Since: 0.2.4.0

Instance details

Defined in Data.SOP.BasicFunctors

Methods

liftReadsPrec2 :: (Int -> ReadS a) -> ReadS [a] -> (Int -> ReadS b) -> ReadS [b] -> Int -> ReadS (K a b) #

liftReadList2 :: (Int -> ReadS a) -> ReadS [a] -> (Int -> ReadS b) -> ReadS [b] -> ReadS [K a b] #

liftReadPrec2 :: ReadPrec a -> ReadPrec [a] -> ReadPrec b -> ReadPrec [b] -> ReadPrec (K a b) #

liftReadListPrec2 :: ReadPrec a -> ReadPrec [a] -> ReadPrec b -> ReadPrec [b] -> ReadPrec [K a b] #

Show2 (K :: Type -> Type -> Type) # | Since: 0.2.4.0
Instance details Defined in Data.SOP.BasicFunctors Methods liftShowsPrec2 :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> (Int -> b -> ShowS) -> ([b] -> ShowS) -> Int -> K a b -> ShowS # liftShowList2 :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> (Int -> b -> ShowS) -> ([b] -> ShowS) -> [K a b] -> ShowS #
NFData2 (K :: Type -> Type -> Type) # | Since: 0.2.5.0
Instance details Defined in Data.SOP.BasicFunctors Methods liftRnf2 :: (a -> ()) -> (b -> ()) -> K a b -> () #
Eq a => Eq1 (K a :: Type -> Type) # | Since: 0.2.4.0
Instance details Defined in Data.SOP.BasicFunctors Methods liftEq :: (a0 -> b -> Bool) -> K a a0 -> K a b -> Bool #
Ord a => Ord1 (K a :: Type -> Type) # | Since: 0.2.4.0
Instance details Defined in Data.SOP.BasicFunctors Methods liftCompare :: (a0 -> b -> Ordering) -> K a a0 -> K a b -> Ordering #
Read a => Read1 (K a :: Type -> Type) # | Since: 0.2.4.0
Instance details Defined in Data.SOP.BasicFunctors Methods liftReadsPrec :: (Int -> ReadS a0) -> ReadS [a0] -> Int -> ReadS (K a a0) # liftReadList :: (Int -> ReadS a0) -> ReadS [a0] -> ReadS [K a a0] # liftReadPrec :: ReadPrec a0 -> ReadPrec [a0] -> ReadPrec (K a a0) # liftReadListPrec :: ReadPrec a0 -> ReadPrec [a0] -> ReadPrec [K a a0] #
Show a => Show1 (K a :: Type -> Type) # | Since: 0.2.4.0
Instance details Defined in Data.SOP.BasicFunctors Methods liftShowsPrec :: (Int -> a0 -> ShowS) -> ([a0] -> ShowS) -> Int -> K a a0 -> ShowS # liftShowList :: (Int -> a0 -> ShowS) -> ([a0] -> ShowS) -> [K a a0] -> ShowS #
NFData a => NFData1 (K a :: Type -> Type) # | Since: 0.2.5.0
Instance details Defined in Data.SOP.BasicFunctors Methods liftRnf :: (a0 -> ()) -> K a a0 -> () #
Monoid a => Applicative (K a :: Type -> Type) # |
Instance details Defined in Data.SOP.BasicFunctors Methods pure :: a0 -> K a a0 # (<*>) :: K a (a0 -> b) -> K a a0 -> K a b # liftA2 :: (a0 -> b -> c) -> K a a0 -> K a b -> K a c # (*>) :: K a a0 -> K a b -> K a b # (<*) :: K a a0 -> K a b -> K a a0 #
Functor (K a :: Type -> Type) # |
Instance details Defined in Data.SOP.BasicFunctors Methods fmap :: (a0 -> b) -> K a a0 -> K a b # (<$) :: a0 -> K a b -> K a a0 #
Foldable (K a :: Type -> Type) # |

Instance details

Defined in Data.SOP.BasicFunctors

Methods

fold :: Monoid m => K a m -> m #

foldMap :: Monoid m => (a0 -> m) -> K a a0 -> m #

foldMap' :: Monoid m => (a0 -> m) -> K a a0 -> m #

foldr :: (a0 -> b -> b) -> b -> K a a0 -> b #

foldr' :: (a0 -> b -> b) -> b -> K a a0 -> b #

foldl :: (b -> a0 -> b) -> b -> K a a0 -> b #

foldl' :: (b -> a0 -> b) -> b -> K a a0 -> b #

foldr1 :: (a0 -> a0 -> a0) -> K a a0 -> a0 #

foldl1 :: (a0 -> a0 -> a0) -> K a a0 -> a0 #

toList :: K a a0 -> [a0] #

null :: K a a0 -> Bool #

length :: K a a0 -> Int #

elem :: Eq a0 => a0 -> K a a0 -> Bool #

maximum :: Ord a0 => K a a0 -> a0 #

minimum :: Ord a0 => K a a0 -> a0 #

sum :: Num a0 => K a a0 -> a0 #

product :: Num a0 => K a a0 -> a0 #

Traversable (K a :: Type -> Type) # |
Instance details Defined in Data.SOP.BasicFunctors Methods traverse :: Applicative f => (a0 -> f b) -> K a a0 -> f (K a b) # sequenceA :: Applicative f => K a (f a0) -> f (K a a0) # mapM :: Monad m => (a0 -> m b) -> K a a0 -> m (K a b) # sequence :: Monad m => K a (m a0) -> m (K a a0) #
NFData a => NFData (K a b) # | Since: 0.2.5.0
Instance details Defined in Data.SOP.BasicFunctors Methods rnf :: K a b -> () #
Monoid a => Monoid (K a b) # | Since: 0.4.0.0
Instance details Defined in Data.SOP.BasicFunctors Methods mempty :: K a b # mappend :: K a b -> K a b -> K a b # mconcat :: [K a b] -> K a b #
Semigroup a => Semigroup (K a b) # | Since: 0.4.0.0
Instance details Defined in Data.SOP.BasicFunctors Methods (<>) :: K a b -> K a b -> K a b # sconcat :: NonEmpty (K a b) -> K a b # stimes :: Integral b0 => b0 -> K a b -> K a b #
Generic (K a b) # |

Instance details

Defined in Data.SOP.BasicFunctors

Associated Types

type Rep (K a b) |
Instance details Defined in Data.SOP.BasicFunctors type Rep (K a b) = D1 ('MetaData "K" "Data.SOP.BasicFunctors" "sop-core-0.5.0.2-3pPdHSIvhiEBpoNP4ADc2R" 'True) (C1 ('MetaCons "K" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 a)))

Methods

from :: K a b -> Rep (K a b) x #

to :: Rep (K a b) x -> K a b #

Read a => Read (K a b) # |
Instance details Defined in Data.SOP.BasicFunctors Methods readsPrec :: Int -> ReadS (K a b) # readList :: ReadS [K a b] # readPrec :: ReadPrec (K a b) # readListPrec :: ReadPrec [K a b] #
Show a => Show (K a b) # |
Instance details Defined in Data.SOP.BasicFunctors Methods showsPrec :: Int -> K a b -> ShowS # show :: K a b -> String # showList :: [K a b] -> ShowS #
Eq a => Eq (K a b) # |
Instance details Defined in Data.SOP.BasicFunctors Methods (==) :: K a b -> K a b -> Bool # (/=) :: K a b -> K a b -> Bool #
Ord a => Ord (K a b) # |
Instance details Defined in Data.SOP.BasicFunctors Methods compare :: K a b -> K a b -> Ordering # (<) :: K a b -> K a b -> Bool # (<=) :: K a b -> K a b -> Bool # (>) :: K a b -> K a b -> Bool # (>=) :: K a b -> K a b -> Bool # max :: K a b -> K a b -> K a b # min :: K a b -> K a b -> K a b #
type Rep (K a b) # |
Instance details Defined in Data.SOP.BasicFunctors type Rep (K a b) = D1 ('MetaData "K" "Data.SOP.BasicFunctors" "sop-core-0.5.0.2-3pPdHSIvhiEBpoNP4ADc2R" 'True) (C1 ('MetaCons "K" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 a)))

unK :: forall {k} a (b :: k). K a b -> a #

Extract the contents of a `K` value.

newtype I a #

The identity type functor.

Like `Identity`, but with a shorter name.

Constructors

I a |

#### Instances

Instances details

Eq1 I # | Since: 0.2.4.0
Instance details Defined in Data.SOP.BasicFunctors Methods liftEq :: (a -> b -> Bool) -> I a -> I b -> Bool #
Ord1 I # | Since: 0.2.4.0
Instance details Defined in Data.SOP.BasicFunctors Methods liftCompare :: (a -> b -> Ordering) -> I a -> I b -> Ordering #
Read1 I # | Since: 0.2.4.0
Instance details Defined in Data.SOP.BasicFunctors Methods liftReadsPrec :: (Int -> ReadS a) -> ReadS [a] -> Int -> ReadS (I a) # liftReadList :: (Int -> ReadS a) -> ReadS [a] -> ReadS [I a] # liftReadPrec :: ReadPrec a -> ReadPrec [a] -> ReadPrec (I a) # liftReadListPrec :: ReadPrec a -> ReadPrec [a] -> ReadPrec [I a] #
Show1 I # | Since: 0.2.4.0
Instance details Defined in Data.SOP.BasicFunctors Methods liftShowsPrec :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> Int -> I a -> ShowS # liftShowList :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> [I a] -> ShowS #
NFData1 I # | Since: 0.2.5.0
Instance details Defined in Data.SOP.BasicFunctors Methods liftRnf :: (a -> ()) -> I a -> () #
Applicative I # |
Instance details Defined in Data.SOP.BasicFunctors Methods pure :: a -> I a # (<*>) :: I (a -> b) -> I a -> I b # liftA2 :: (a -> b -> c) -> I a -> I b -> I c # (*>) :: I a -> I b -> I b # (<*) :: I a -> I b -> I a #
Functor I # |
Instance details Defined in Data.SOP.BasicFunctors Methods fmap :: (a -> b) -> I a -> I b # (<$) :: a -> I b -> I a #
Monad I # |
Instance details Defined in Data.SOP.BasicFunctors Methods (>>=) :: I a -> (a -> I b) -> I b # (>>) :: I a -> I b -> I b # return :: a -> I a #
Foldable I # |

Instance details

Defined in Data.SOP.BasicFunctors

Methods

fold :: Monoid m => I m -> m #

foldMap :: Monoid m => (a -> m) -> I a -> m #

foldMap' :: Monoid m => (a -> m) -> I a -> m #

foldr :: (a -> b -> b) -> b -> I a -> b #

foldr' :: (a -> b -> b) -> b -> I a -> b #

foldl :: (b -> a -> b) -> b -> I a -> b #

foldl' :: (b -> a -> b) -> b -> I a -> b #

foldr1 :: (a -> a -> a) -> I a -> a #

foldl1 :: (a -> a -> a) -> I a -> a #

toList :: I a -> [a] #

null :: I a -> Bool #

length :: I a -> Int #

elem :: Eq a => a -> I a -> Bool #

maximum :: Ord a => I a -> a #

minimum :: Ord a => I a -> a #

sum :: Num a => I a -> a #

product :: Num a => I a -> a #

Traversable I # |
Instance details Defined in Data.SOP.BasicFunctors Methods traverse :: Applicative f => (a -> f b) -> I a -> f (I b) # sequenceA :: Applicative f => I (f a) -> f (I a) # mapM :: Monad m => (a -> m b) -> I a -> m (I b) # sequence :: Monad m => I (m a) -> m (I a) #
NFData a => NFData (I a) # | Since: 0.2.5.0
Instance details Defined in Data.SOP.BasicFunctors Methods rnf :: I a -> () #
Monoid a => Monoid (I a) # | Since: 0.4.0.0
Instance details Defined in Data.SOP.BasicFunctors Methods mempty :: I a # mappend :: I a -> I a -> I a # mconcat :: [I a] -> I a #
Semigroup a => Semigroup (I a) # | Since: 0.4.0.0
Instance details Defined in Data.SOP.BasicFunctors Methods (<>) :: I a -> I a -> I a # sconcat :: NonEmpty (I a) -> I a # stimes :: Integral b => b -> I a -> I a #
Generic (I a) # |

Instance details

Defined in Data.SOP.BasicFunctors

Associated Types

type Rep (I a) |
Instance details Defined in Data.SOP.BasicFunctors type Rep (I a) = D1 ('MetaData "I" "Data.SOP.BasicFunctors" "sop-core-0.5.0.2-3pPdHSIvhiEBpoNP4ADc2R" 'True) (C1 ('MetaCons "I" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 a)))

Methods

from :: I a -> Rep (I a) x #

to :: Rep (I a) x -> I a #

Read a => Read (I a) # |
Instance details Defined in Data.SOP.BasicFunctors Methods readsPrec :: Int -> ReadS (I a) # readList :: ReadS [I a] # readPrec :: ReadPrec (I a) # readListPrec :: ReadPrec [I a] #
Show a => Show (I a) # |
Instance details Defined in Data.SOP.BasicFunctors Methods showsPrec :: Int -> I a -> ShowS # show :: I a -> String # showList :: [I a] -> ShowS #
Eq a => Eq (I a) # |
Instance details Defined in Data.SOP.BasicFunctors Methods (==) :: I a -> I a -> Bool # (/=) :: I a -> I a -> Bool #
Ord a => Ord (I a) # |
Instance details Defined in Data.SOP.BasicFunctors Methods compare :: I a -> I a -> Ordering # (<) :: I a -> I a -> Bool # (<=) :: I a -> I a -> Bool # (>) :: I a -> I a -> Bool # (>=) :: I a -> I a -> Bool # max :: I a -> I a -> I a # min :: I a -> I a -> I a #
type Rep (I a) # |
Instance details Defined in Data.SOP.BasicFunctors type Rep (I a) = D1 ('MetaData "I" "Data.SOP.BasicFunctors" "sop-core-0.5.0.2-3pPdHSIvhiEBpoNP4ADc2R" 'True) (C1 ('MetaCons "I" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 a)))

unI :: I a -> a #

Extract the contents of an `I` value.

newtype ((f :: l -> Type) :.: (g :: k -> l)) (p :: k) infixr 7 #

Composition of functors.

Like `Compose`, but kind-polymorphic and with a shorter name.

Constructors

Comp (f (g p)) |

#### Instances

Instances details

(Eq1 f, Eq1 g) => Eq1 (f :.: g) # | Since: 0.2.4.0
Instance details Defined in Data.SOP.BasicFunctors Methods liftEq :: (a -> b -> Bool) -> (f :.: g) a -> (f :.: g) b -> Bool #
(Ord1 f, Ord1 g) => Ord1 (f :.: g) # | Since: 0.2.4.0
Instance details Defined in Data.SOP.BasicFunctors Methods liftCompare :: (a -> b -> Ordering) -> (f :.: g) a -> (f :.: g) b -> Ordering #
(Read1 f, Read1 g) => Read1 (f :.: g) # | Since: 0.2.4.0
Instance details Defined in Data.SOP.BasicFunctors Methods liftReadsPrec :: (Int -> ReadS a) -> ReadS [a] -> Int -> ReadS ((f :.: g) a) # liftReadList :: (Int -> ReadS a) -> ReadS [a] -> ReadS [(f :.: g) a] # liftReadPrec :: ReadPrec a -> ReadPrec [a] -> ReadPrec ((f :.: g) a) # liftReadListPrec :: ReadPrec a -> ReadPrec [a] -> ReadPrec [(f :.: g) a] #
(Show1 f, Show1 g) => Show1 (f :.: g) # | Since: 0.2.4.0
Instance details Defined in Data.SOP.BasicFunctors Methods liftShowsPrec :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> Int -> (f :.: g) a -> ShowS # liftShowList :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> [(f :.: g) a] -> ShowS #
(NFData1 f, NFData1 g) => NFData1 (f :.: g) # | Since: 0.2.5.0
Instance details Defined in Data.SOP.BasicFunctors Methods liftRnf :: (a -> ()) -> (f :.: g) a -> () #
(Applicative f, Applicative g) => Applicative (f :.: g) # | Since: 0.2.5.0
Instance details Defined in Data.SOP.BasicFunctors Methods pure :: a -> (f :.: g) a # (<*>) :: (f :.: g) (a -> b) -> (f :.: g) a -> (f :.: g) b # liftA2 :: (a -> b -> c) -> (f :.: g) a -> (f :.: g) b -> (f :.: g) c # (*>) :: (f :.: g) a -> (f :.: g) b -> (f :.: g) b # (<*) :: (f :.: g) a -> (f :.: g) b -> (f :.: g) a #
(Functor f, Functor g) => Functor (f :.: g) # |
Instance details Defined in Data.SOP.BasicFunctors Methods fmap :: (a -> b) -> (f :.: g) a -> (f :.: g) b # (<$) :: a -> (f :.: g) b -> (f :.: g) a #
(Foldable f, Foldable g) => Foldable (f :.: g) # | Since: 0.2.5.0

Instance details

Defined in Data.SOP.BasicFunctors

Methods

fold :: Monoid m => (f :.: g) m -> m #

foldMap :: Monoid m => (a -> m) -> (f :.: g) a -> m #

foldMap' :: Monoid m => (a -> m) -> (f :.: g) a -> m #

foldr :: (a -> b -> b) -> b -> (f :.: g) a -> b #

foldr' :: (a -> b -> b) -> b -> (f :.: g) a -> b #

foldl :: (b -> a -> b) -> b -> (f :.: g) a -> b #

foldl' :: (b -> a -> b) -> b -> (f :.: g) a -> b #

foldr1 :: (a -> a -> a) -> (f :.: g) a -> a #

foldl1 :: (a -> a -> a) -> (f :.: g) a -> a #

toList :: (f :.: g) a -> [a] #

null :: (f :.: g) a -> Bool #

length :: (f :.: g) a -> Int #

elem :: Eq a => a -> (f :.: g) a -> Bool #

maximum :: Ord a => (f :.: g) a -> a #

minimum :: Ord a => (f :.: g) a -> a #

sum :: Num a => (f :.: g) a -> a #

product :: Num a => (f :.: g) a -> a #

(Traversable f, Traversable g) => Traversable (f :.: g) # | Since: 0.2.5.0
Instance details Defined in Data.SOP.BasicFunctors Methods traverse :: Applicative f0 => (a -> f0 b) -> (f :.: g) a -> f0 ((f :.: g) b) # sequenceA :: Applicative f0 => (f :.: g) (f0 a) -> f0 ((f :.: g) a) # mapM :: Monad m => (a -> m b) -> (f :.: g) a -> m ((f :.: g) b) # sequence :: Monad m => (f :.: g) (m a) -> m ((f :.: g) a) #
NFData (f (g a)) => NFData ((f :.: g) a) # | Since: 0.2.5.0
Instance details Defined in Data.SOP.BasicFunctors Methods rnf :: (f :.: g) a -> () #
Monoid (f (g x)) => Monoid ((f :.: g) x) # | Since: 0.4.0.0
Instance details Defined in Data.SOP.BasicFunctors Methods mempty :: (f :.: g) x # mappend :: (f :.: g) x -> (f :.: g) x -> (f :.: g) x # mconcat :: [(f :.: g) x] -> (f :.: g) x #
Semigroup (f (g x)) => Semigroup ((f :.: g) x) # | Since: 0.4.0.0
Instance details Defined in Data.SOP.BasicFunctors Methods (<>) :: (f :.: g) x -> (f :.: g) x -> (f :.: g) x # sconcat :: NonEmpty ((f :.: g) x) -> (f :.: g) x # stimes :: Integral b => b -> (f :.: g) x -> (f :.: g) x #
Generic ((f :.: g) p) # |

Instance details

Defined in Data.SOP.BasicFunctors

Associated Types

type Rep ((f :.: g) p) |
Instance details Defined in Data.SOP.BasicFunctors type Rep ((f :.: g) p) = D1 ('MetaData ":.:" "Data.SOP.BasicFunctors" "sop-core-0.5.0.2-3pPdHSIvhiEBpoNP4ADc2R" 'True) (C1 ('MetaCons "Comp" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 (f (g p)))))

Methods

from :: (f :.: g) p -> Rep ((f :.: g) p) x #

to :: Rep ((f :.: g) p) x -> (f :.: g) p #

(Read1 f, Read1 g, Read a) => Read ((f :.: g) a) # |
Instance details Defined in Data.SOP.BasicFunctors Methods readsPrec :: Int -> ReadS ((f :.: g) a) # readList :: ReadS [(f :.: g) a] # readPrec :: ReadPrec ((f :.: g) a) # readListPrec :: ReadPrec [(f :.: g) a] #
(Show1 f, Show1 g, Show a) => Show ((f :.: g) a) # |
Instance details Defined in Data.SOP.BasicFunctors Methods showsPrec :: Int -> (f :.: g) a -> ShowS # show :: (f :.: g) a -> String # showList :: [(f :.: g) a] -> ShowS #
(Eq1 f, Eq1 g, Eq a) => Eq ((f :.: g) a) # |
Instance details Defined in Data.SOP.BasicFunctors Methods (==) :: (f :.: g) a -> (f :.: g) a -> Bool # (/=) :: (f :.: g) a -> (f :.: g) a -> Bool #
(Ord1 f, Ord1 g, Ord a) => Ord ((f :.: g) a) # |
Instance details Defined in Data.SOP.BasicFunctors Methods compare :: (f :.: g) a -> (f :.: g) a -> Ordering # (<) :: (f :.: g) a -> (f :.: g) a -> Bool # (<=) :: (f :.: g) a -> (f :.: g) a -> Bool # (>) :: (f :.: g) a -> (f :.: g) a -> Bool # (>=) :: (f :.: g) a -> (f :.: g) a -> Bool # max :: (f :.: g) a -> (f :.: g) a -> (f :.: g) a # min :: (f :.: g) a -> (f :.: g) a -> (f :.: g) a #
type Rep ((f :.: g) p) # |
Instance details Defined in Data.SOP.BasicFunctors type Rep ((f :.: g) p) = D1 ('MetaData ":.:" "Data.SOP.BasicFunctors" "sop-core-0.5.0.2-3pPdHSIvhiEBpoNP4ADc2R" 'True) (C1 ('MetaCons "Comp" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 (f (g p)))))

unComp :: forall {l} {k} f (g :: k -> l) (p :: k). (f :.: g) p -> f (g p) #

Extract the contents of a `Comp` value.

### Mapping functions

mapII :: (a -> b) -> I a -> I b #

Lift the given function.

Since: 0.2.5.0

mapIK :: forall {k} a b (c :: k). (a -> b) -> I a -> K b c #

Lift the given function.

Since: 0.2.5.0

mapKI :: forall {k} a b (c :: k). (a -> b) -> K a c -> I b #

Lift the given function.

Since: 0.2.5.0

mapKK :: forall {k1} {k2} a b (c :: k1) (d :: k2). (a -> b) -> K a c -> K b d #

Lift the given function.

Since: 0.2.5.0

mapIII :: (a -> b -> c) -> I a -> I b -> I c #

Lift the given function.

Since: 0.2.5.0

mapIIK :: forall {k} a b c (d :: k). (a -> b -> c) -> I a -> I b -> K c d #

Lift the given function.

Since: 0.2.5.0

mapIKI :: forall {k} a b c (d :: k). (a -> b -> c) -> I a -> K b d -> I c #

Lift the given function.

Since: 0.2.5.0

mapIKK :: forall {k1} {k2} a b c (d :: k1) (e :: k2). (a -> b -> c) -> I a -> K b d -> K c e #

Lift the given function.

Since: 0.2.5.0

mapKII :: forall {k} a b c (d :: k). (a -> b -> c) -> K a d -> I b -> I c #

Lift the given function.

Since: 0.2.5.0

mapKIK :: forall {k1} {k2} a b c (d :: k1) (e :: k2). (a -> b -> c) -> K a d -> I b -> K c e #

Lift the given function.

Since: 0.2.5.0

mapKKI :: forall {k1} {k2} a b c (d :: k1) (e :: k2). (a -> b -> c) -> K a d -> K b e -> I c #

Lift the given function.

Since: 0.2.5.0

mapKKK :: forall {k1} {k2} {k3} a b c (d :: k1) (e :: k2) (f :: k3). (a -> b -> c) -> K a d -> K b e -> K c f #

Lift the given function.

Since: 0.2.5.0

## Mapping constraints

class (AllF c xs, SListI xs) => All (c :: k -> Constraint) (xs :: [k]) #

Require a constraint for every element of a list.

If you have a datatype that is indexed over a type-level list, then you can use `All` to indicate that all elements of that type-level list must satisfy a given constraint.

Example: The constraint

    All Eq '[ Int, Bool, Char ]

is equivalent to the constraint

    (Eq Int, Eq Bool, Eq Char)

Example: A type signature such as

    f :: All Eq xs => NP I xs -> ...

means that `f` can assume that all elements of the n-ary product satisfy `Eq`.

Note on superclasses: ghc cannot deduce superclasses from `All` constraints. You might expect the following to compile

    class (Eq a) => MyClass a

    foo :: (All Eq xs) => NP f xs -> z
    foo = [..]

    bar :: (All MyClass xs) => NP f xs -> x
    bar = foo

but it will fail with an error saying that it was unable to deduce the class constraint ``AllF` `Eq` xs` (or similar) in the definition of `bar`. In cases like this you can use `Dict` from Data.SOP.Dict to prove conversions between constraints. See this answer on SO for more details.

Minimal complete definition

cpara_SList

#### Instances

Instances details

All (c :: k -> Constraint) ('[] :: [k]) # |
Instance details Defined in Data.SOP.Constraint Methods cpara_SList :: proxy c -> r ('[] :: [k]) -> (forall (y :: k) (ys :: [k]). (c y, All c ys) => r ys -> r (y ': ys)) -> r ('[] :: [k]) #
(c x, All c xs) => All (c :: a -> Constraint) (x ': xs :: [a]) # |
Instance details Defined in Data.SOP.Constraint Methods cpara_SList :: proxy c -> r ('[] :: [a]) -> (forall (y :: a) (ys :: [a]). (c y, All c ys) => r ys -> r (y ': ys)) -> r (x ': xs) #

type All2 (c :: k -> Constraint) = All (All c) #

Require a constraint for every element of a list of lists.

If you have a datatype that is indexed over a type-level list of lists, then you can use `All2` to indicate that all elements of the inner lists must satisfy a given constraint.

Example: The constraint

    All2 Eq '[ '[ Int ], '[ Bool, Char ] ]

is equivalent to the constraint

    (Eq Int, Eq Bool, Eq Char)

Example: A type signature such as

    f :: All2 Eq xss => SOP I xs -> ...

means that `f` can assume that all elements of the sum of product satisfy `Eq`.

Since 0.4.0.0, this is merely a synonym for 'All (All c)'.

Since: 0.4.0.0

cpara_SList :: All c xs => proxy c -> r ('[] :: [k]) -> (forall (y :: k) (ys :: [k]). (c y, All c ys) => r ys -> r (y ': ys)) -> r xs #

Constrained paramorphism for a type-level list.

The advantage of writing functions in terms of `cpara_SList` is that they are then typically not recursive, and can be unfolded statically if the type-level list is statically known.

Since: 0.4.0.0

ccase_SList :: forall {a} c (xs :: [a]) proxy r. All c xs => proxy c -> r ('[] :: [a]) -> (forall (y :: a) (ys :: [a]). (c y, All c ys) => r (y ': ys)) -> r xs #

Constrained case distinction on a type-level list.

Since: 0.4.0.0

class (SListI xs, SListI ys, SameShapeAs xs ys, SameShapeAs ys xs, AllZipF c xs ys) => AllZip (c :: a -> b -> Constraint) (xs :: [a]) (ys :: [b]) #

Require a constraint pointwise for every pair of elements from two lists.

Example: The constraint

    AllZip (~) '[ Int, Bool, Char ] '[ a, b, c ]

is equivalent to the constraint

    (Int ~ a, Bool ~ b, Char ~ c)

Since: 0.3.1.0

#### Instances

Instances details

(SListI xs, SListI ys, SameShapeAs xs ys, SameShapeAs ys xs, AllZipF c xs ys) => AllZip (c :: a -> b -> Constraint) (xs :: [a]) (ys :: [b]) # |
Instance details Defined in Data.SOP.Constraint

class (AllZipF (AllZip f) xss yss, SListI xss, SListI yss, SameShapeAs xss yss, SameShapeAs yss xss) => AllZip2 (f :: a -> b -> Constraint) (xss :: [[a]]) (yss :: [[b]]) #

Require a constraint pointwise for every pair of elements from two lists of lists.

#### Instances

Instances details

(AllZipF (AllZip f) xss yss, SListI xss, SListI yss, SameShapeAs xss yss, SameShapeAs yss xss) => AllZip2 (f :: a -> b -> Constraint) (xss :: [[a]]) (yss :: [[b]]) # |
Instance details Defined in Data.SOP.Constraint

type family AllN (h :: (k -> Type) -> l -> Type) (c :: k -> Constraint) :: l -> Constraint #

A generalization of `All` and `All2`.

The family `AllN` expands to `All` or `All2` depending on whether the argument is indexed by a list or a list of lists.

#### Instances

Instances details

type AllN (POP :: (k -> Type) -> [[k]] -> Type) (c :: k -> Constraint) # |
Instance details Defined in Data.SOP.NP type AllN (POP :: (k -> Type) -> [[k]] -> Type) (c :: k -> Constraint) = All2 c
type AllN (SOP :: (k -> Type) -> [[k]] -> Type) (c :: k -> Constraint) # |
Instance details Defined in Data.SOP.NS type AllN (SOP :: (k -> Type) -> [[k]] -> Type) (c :: k -> Constraint) = All2 c
type AllN (NP :: (k -> Type) -> [k] -> Type) (c :: k -> Constraint) # |
Instance details Defined in Data.SOP.NP type AllN (NP :: (k -> Type) -> [k] -> Type) (c :: k -> Constraint) = All c
type AllN (NS :: (k -> Type) -> [k] -> Type) (c :: k -> Constraint) # |
Instance details Defined in Data.SOP.NS type AllN (NS :: (k -> Type) -> [k] -> Type) (c :: k -> Constraint) = All c

type family AllZipN (h :: (k -> Type) -> l -> Type) (c :: k1 -> k2 -> Constraint) :: l1 -> l2 -> Constraint #

A generalization of `AllZip` and `AllZip2`.

The family `AllZipN` expands to `AllZip` or `AllZip2` depending on whther the argument is indexed by a list or a list of lists.

#### Instances

Instances details

type AllZipN (POP :: (k -> Type) -> [[k]] -> Type) (c :: a -> b -> Constraint) # |
Instance details Defined in Data.SOP.NP type AllZipN (POP :: (k -> Type) -> [[k]] -> Type) (c :: a -> b -> Constraint) = AllZip2 c
type AllZipN (NP :: (k -> Type) -> [k] -> Type) (c :: a -> b -> Constraint) # |
Instance details Defined in Data.SOP.NP type AllZipN (NP :: (k -> Type) -> [k] -> Type) (c :: a -> b -> Constraint) = AllZip c

## Other constraints

class f (g x) => Compose (f :: k -> Constraint) (g :: k1 -> k) (x :: k1) infixr 9 #

Composition of constraints.

Note that the result of the composition must be a constraint, and therefore, in ``Compose` f g`, the kind of `f` is `k -> `Constraint``. The kind of `g`, however, is `l -> k` and can thus be a normal type constructor.

A typical use case is in connection with `All` on an `NP` or an `NS`. For example, in order to denote that all elements on an ``NP` f xs` satisfy `Show`, we can say ``All` (`Compose` `Show` f) xs`.

Since: 0.2

#### Instances

Instances details

f (g x) => Compose (f :: k1 -> Constraint) (g :: k2 -> k1) (x :: k2) # |
Instance details Defined in Data.SOP.Constraint

class (f x, g x) => And (f :: k -> Constraint) (g :: k -> Constraint) (x :: k) infixl 7 #

Pairing of constraints.

Since: 0.2

#### Instances

Instances details

(f x, g x) => And (f :: k -> Constraint) (g :: k -> Constraint) (x :: k) # |
Instance details Defined in Data.SOP.Constraint

class Top (x :: k) #

A constraint that can always be satisfied.

Since: 0.2

#### Instances

Instances details

Top (x :: k) # |
Instance details Defined in Data.SOP.Constraint

class Coercible (f x) (g y) => LiftedCoercible (f :: k -> k1) (g :: k2 -> k1) (x :: k) (y :: k2) #

The constraint ``LiftedCoercible` f g x y` is equivalent to ``Coercible` (f x) (g y)`.

Since: 0.3.1.0

#### Instances

Instances details

Coercible (f x) (g y) => LiftedCoercible (f :: k1 -> k2) (g :: k3 -> k2) (x :: k1) (y :: k3) # |
Instance details Defined in Data.SOP.Constraint

type family SameShapeAs (xs :: [a]) (ys :: [b]) where ... #

Type family that forces a type-level list to be of the same shape as the given type-level list.

Since 0.5.0.0, this only tests the top-level structure of the list, and is intended to be used in conjunction with a separate construct (such as the `AllZip`, `AllZipF` combination to tie the recursive knot). The reason is that making `SameShapeAs` directly recursive leads to quadratic compile times.

The main use of this constraint is to help type inference to learn something about otherwise unknown type-level lists.

Since: 0.5.0.0

Equations

SameShapeAs ('[] :: [a]) (ys :: [b]) = ys ~ ('[] :: [b]) |
SameShapeAs (x ': xs :: [a1]) (ys :: [a2]) = ys ~ (Head ys ': Tail ys) |

## Singletons

data SList (a :: [k]) where #

Explicit singleton list.

A singleton list can be used to reveal the structure of a type-level list argument that the function is quantified over. For every type-level list `xs`, there is one non-bottom value of type ``SList` xs`.

Note that these singleton lists are polymorphic in the list elements; we do not require a singleton representation for them.

Since: 0.2

Constructors

SNil :: forall {k}. SList ('[] :: [k]) |
SCons :: forall {k} (xs :: [k]) (x :: k). SListI xs => SList (x ': xs) |

#### Instances

Instances details

Show (SList xs) # |
Instance details Defined in Data.SOP.Sing Methods showsPrec :: Int -> SList xs -> ShowS # show :: SList xs -> String # showList :: [SList xs] -> ShowS #
Eq (SList xs) # |
Instance details Defined in Data.SOP.Sing Methods (==) :: SList xs -> SList xs -> Bool # (/=) :: SList xs -> SList xs -> Bool #
Ord (SList xs) # |
Instance details Defined in Data.SOP.Sing Methods compare :: SList xs -> SList xs -> Ordering # (<) :: SList xs -> SList xs -> Bool # (<=) :: SList xs -> SList xs -> Bool # (>) :: SList xs -> SList xs -> Bool # (>=) :: SList xs -> SList xs -> Bool # max :: SList xs -> SList xs -> SList xs # min :: SList xs -> SList xs -> SList xs #

type SListI = All (Top :: k -> Constraint) #

Implicit singleton list.

A singleton list can be used to reveal the structure of a type-level list argument that the function is quantified over.

Since 0.4.0.0, this is now defined in terms of `All`. A singleton list provides a witness for a type-level list where the elements need not satisfy any additional constraints.

Since: 0.4.0.0

type SListI2 = All (SListI :: [k] -> Constraint) #

Require a singleton for every inner list in a list of lists.

sList :: forall {k} (xs :: [k]). SListI xs => SList xs #

Get hold of an explicit singleton (that one can then pattern match on) for a type-level list

para_SList :: forall {a} (xs :: [a]) r. SListI xs => r ('[] :: [a]) -> (forall (y :: a) (ys :: [a]). SListI ys => r ys -> r (y ': ys)) -> r xs #

Paramorphism for a type-level list.

Since: 0.4.0.0

case_SList :: forall {a} (xs :: [a]) r. SListI xs => r ('[] :: [a]) -> (forall (y :: a) (ys :: [a]). SListI ys => r (y ': ys)) -> r xs #

Case distinction on a type-level list.

Since: 0.4.0.0

### Shape of type-level lists

data Shape (a :: [k]) where #

Occasionally it is useful to have an explicit, term-level, representation of type-level lists (esp because of https://ghc.haskell.org/trac/ghc/ticket/9108 )

Constructors

ShapeNil :: forall {k}. Shape ('[] :: [k]) |
ShapeCons :: forall {k} (xs :: [k]) (x :: k). SListI xs => Shape xs -> Shape (x ': xs) |

#### Instances

Instances details

Show (Shape xs) # |
Instance details Defined in Data.SOP.Sing Methods showsPrec :: Int -> Shape xs -> ShowS # show :: Shape xs -> String # showList :: [Shape xs] -> ShowS #
Eq (Shape xs) # |
Instance details Defined in Data.SOP.Sing Methods (==) :: Shape xs -> Shape xs -> Bool # (/=) :: Shape xs -> Shape xs -> Bool #
Ord (Shape xs) # |
Instance details Defined in Data.SOP.Sing Methods compare :: Shape xs -> Shape xs -> Ordering # (<) :: Shape xs -> Shape xs -> Bool # (<=) :: Shape xs -> Shape xs -> Bool # (>) :: Shape xs -> Shape xs -> Bool # (>=) :: Shape xs -> Shape xs -> Bool # max :: Shape xs -> Shape xs -> Shape xs # min :: Shape xs -> Shape xs -> Shape xs #

shape :: forall k (xs :: [k]). SListI xs => Shape xs #

The shape of a type-level list.

lengthSList :: forall k (xs :: [k]) proxy. SListI xs => proxy xs -> Int #

The length of a type-level list.

Since: 0.2

## Re-exports

data Proxy (t :: k) #

`Proxy` is a type that holds no data, but has a phantom parameter of arbitrary type (or even kind). Its use is to provide type information, even though there is no value available of that type (or it may be too costly to create one).

Historically, ``Proxy` :: `Proxy` a` is a safer alternative to the ``undefined` :: a` idiom.

    >>> Proxy :: Proxy (Void, Int -> Int)
    Proxy

Proxy can even hold types of higher kinds,

    >>> Proxy :: Proxy Either
    Proxy

    >>> Proxy :: Proxy Functor
    Proxy

    >>> Proxy :: Proxy complicatedStructure
    Proxy

Constructors

Proxy |

#### Instances

Instances details

Generic1 (Proxy :: k -> Type) |

Instance details

Defined in GHC.Internal.Generics

Associated Types

type Rep1 (Proxy :: k -> Type) | @since base-4.6.0.0
Instance details Defined in GHC.Internal.Generics type Rep1 (Proxy :: k -> Type) = D1 ('MetaData "Proxy" "GHC.Internal.Data.Proxy" "ghc-internal" 'False) (C1 ('MetaCons "Proxy" 'PrefixI 'False) (U1 :: k -> Type))

Methods

from1 :: forall (a :: k). Proxy a -> Rep1 (Proxy :: k -> Type) a #

to1 :: forall (a :: k). Rep1 (Proxy :: k -> Type) a -> Proxy a #

MonadZip (Proxy :: Type -> Type) | Since: base-4.9.0.0
Instance details Defined in Control.Monad.Zip Methods mzip :: Proxy a -> Proxy b -> Proxy (a, b) # mzipWith :: (a -> b -> c) -> Proxy a -> Proxy b -> Proxy c # munzip :: Proxy (a, b) -> (Proxy a, Proxy b) #
Eq1 (Proxy :: Type -> Type) | Since: base-4.9.0.0
Instance details Defined in Data.Functor.Classes Methods liftEq :: (a -> b -> Bool) -> Proxy a -> Proxy b -> Bool #
Ord1 (Proxy :: Type -> Type) | Since: base-4.9.0.0
Instance details Defined in Data.Functor.Classes Methods liftCompare :: (a -> b -> Ordering) -> Proxy a -> Proxy b -> Ordering #
Read1 (Proxy :: Type -> Type) | Since: base-4.9.0.0
Instance details Defined in Data.Functor.Classes Methods liftReadsPrec :: (Int -> ReadS a) -> ReadS [a] -> Int -> ReadS (Proxy a) # liftReadList :: (Int -> ReadS a) -> ReadS [a] -> ReadS [Proxy a] # liftReadPrec :: ReadPrec a -> ReadPrec [a] -> ReadPrec (Proxy a) # liftReadListPrec :: ReadPrec a -> ReadPrec [a] -> ReadPrec [Proxy a] #
Show1 (Proxy :: Type -> Type) | Since: base-4.9.0.0
Instance details Defined in Data.Functor.Classes Methods liftShowsPrec :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> Int -> Proxy a -> ShowS # liftShowList :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> [Proxy a] -> ShowS #
Contravariant (Proxy :: Type -> Type) |
Instance details Defined in Data.Functor.Contravariant Methods contramap :: (a' -> a) -> Proxy a -> Proxy a' # (>$) :: b -> Proxy b -> Proxy a #
NFData1 (Proxy :: Type -> Type) | Since: deepseq-1.4.3.0
Instance details Defined in Control.DeepSeq Methods liftRnf :: (a -> ()) -> Proxy a -> () #
Alternative (Proxy :: Type -> Type) | @since base-4.9.0.0
Instance details Defined in GHC.Internal.Data.Proxy Methods empty :: Proxy a # (<|>) :: Proxy a -> Proxy a -> Proxy a # some :: Proxy a -> Proxy [a] # many :: Proxy a -> Proxy [a] #
Applicative (Proxy :: Type -> Type) | @since base-4.7.0.0
Instance details Defined in GHC.Internal.Data.Proxy Methods pure :: a -> Proxy a # (<*>) :: Proxy (a -> b) -> Proxy a -> Proxy b # liftA2 :: (a -> b -> c) -> Proxy a -> Proxy b -> Proxy c # (*>) :: Proxy a -> Proxy b -> Proxy b # (<*) :: Proxy a -> Proxy b -> Proxy a #
Functor (Proxy :: Type -> Type) | @since base-4.7.0.0
Instance details Defined in GHC.Internal.Data.Proxy Methods fmap :: (a -> b) -> Proxy a -> Proxy b # (<$) :: a -> Proxy b -> Proxy a #
Monad (Proxy :: Type -> Type) | @since base-4.7.0.0
Instance details Defined in GHC.Internal.Data.Proxy Methods (>>=) :: Proxy a -> (a -> Proxy b) -> Proxy b # (>>) :: Proxy a -> Proxy b -> Proxy b # return :: a -> Proxy a #
MonadPlus (Proxy :: Type -> Type) | @since base-4.9.0.0
Instance details Defined in GHC.Internal.Data.Proxy Methods mzero :: Proxy a # mplus :: Proxy a -> Proxy a -> Proxy a #
Foldable (Proxy :: Type -> Type) | @since base-4.7.0.0

Instance details

Defined in GHC.Internal.Data.Foldable

Methods

fold :: Monoid m => Proxy m -> m #

foldMap :: Monoid m => (a -> m) -> Proxy a -> m #

foldMap' :: Monoid m => (a -> m) -> Proxy a -> m #

foldr :: (a -> b -> b) -> b -> Proxy a -> b #

foldr' :: (a -> b -> b) -> b -> Proxy a -> b #

foldl :: (b -> a -> b) -> b -> Proxy a -> b #

foldl' :: (b -> a -> b) -> b -> Proxy a -> b #

foldr1 :: (a -> a -> a) -> Proxy a -> a #

foldl1 :: (a -> a -> a) -> Proxy a -> a #

toList :: Proxy a -> [a] #

null :: Proxy a -> Bool #

length :: Proxy a -> Int #

elem :: Eq a => a -> Proxy a -> Bool #

maximum :: Ord a => Proxy a -> a #

minimum :: Ord a => Proxy a -> a #

sum :: Num a => Proxy a -> a #

product :: Num a => Proxy a -> a #

Traversable (Proxy :: Type -> Type) | @since base-4.7.0.0
Instance details Defined in GHC.Internal.Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> Proxy a -> f (Proxy b) # sequenceA :: Applicative f => Proxy (f a) -> f (Proxy a) # mapM :: Monad m => (a -> m b) -> Proxy a -> m (Proxy b) # sequence :: Monad m => Proxy (m a) -> m (Proxy a) #
NFData (Proxy a) | Since: deepseq-1.4.0.0
Instance details Defined in Control.DeepSeq Methods rnf :: Proxy a -> () #
Monoid (Proxy s) | @since base-4.7.0.0
Instance details Defined in GHC.Internal.Data.Proxy Methods mempty :: Proxy s # mappend :: Proxy s -> Proxy s -> Proxy s # mconcat :: [Proxy s] -> Proxy s #
Semigroup (Proxy s) | @since base-4.9.0.0
Instance details Defined in GHC.Internal.Data.Proxy Methods (<>) :: Proxy s -> Proxy s -> Proxy s # sconcat :: NonEmpty (Proxy s) -> Proxy s # stimes :: Integral b => b -> Proxy s -> Proxy s #
Bounded (Proxy t) | @since base-4.7.0.0
Instance details Defined in GHC.Internal.Data.Proxy Methods minBound :: Proxy t # maxBound :: Proxy t #
Enum (Proxy s) | @since base-4.7.0.0
Instance details Defined in GHC.Internal.Data.Proxy Methods succ :: Proxy s -> Proxy s # pred :: Proxy s -> Proxy s # toEnum :: Int -> Proxy s # fromEnum :: Proxy s -> Int # enumFrom :: Proxy s -> [Proxy s] # enumFromThen :: Proxy s -> Proxy s -> [Proxy s] # enumFromTo :: Proxy s -> Proxy s -> [Proxy s] # enumFromThenTo :: Proxy s -> Proxy s -> Proxy s -> [Proxy s] #
Generic (Proxy t) |

Instance details

Defined in GHC.Internal.Generics

Associated Types

type Rep (Proxy t) | @since base-4.6.0.0
Instance details Defined in GHC.Internal.Generics type Rep (Proxy t) = D1 ('MetaData "Proxy" "GHC.Internal.Data.Proxy" "ghc-internal" 'False) (C1 ('MetaCons "Proxy" 'PrefixI 'False) (U1 :: Type -> Type))

Methods

from :: Proxy t -> Rep (Proxy t) x #

to :: Rep (Proxy t) x -> Proxy t #

Ix (Proxy s) | @since base-4.7.0.0
Instance details Defined in GHC.Internal.Data.Proxy Methods range :: (Proxy s, Proxy s) -> [Proxy s] # index :: (Proxy s, Proxy s) -> Proxy s -> Int # unsafeIndex :: (Proxy s, Proxy s) -> Proxy s -> Int # inRange :: (Proxy s, Proxy s) -> Proxy s -> Bool # rangeSize :: (Proxy s, Proxy s) -> Int # unsafeRangeSize :: (Proxy s, Proxy s) -> Int #
Read (Proxy t) | @since base-4.7.0.0
Instance details Defined in GHC.Internal.Data.Proxy Methods readsPrec :: Int -> ReadS (Proxy t) # readList :: ReadS [Proxy t] # readPrec :: ReadPrec (Proxy t) # readListPrec :: ReadPrec [Proxy t] #
Show (Proxy s) | @since base-4.7.0.0
Instance details Defined in GHC.Internal.Data.Proxy Methods showsPrec :: Int -> Proxy s -> ShowS # show :: Proxy s -> String # showList :: [Proxy s] -> ShowS #
Eq (Proxy s) | @since base-4.7.0.0
Instance details Defined in GHC.Internal.Data.Proxy Methods (==) :: Proxy s -> Proxy s -> Bool # (/=) :: Proxy s -> Proxy s -> Bool #
Ord (Proxy s) | @since base-4.7.0.0
Instance details Defined in GHC.Internal.Data.Proxy Methods compare :: Proxy s -> Proxy s -> Ordering # (<) :: Proxy s -> Proxy s -> Bool # (<=) :: Proxy s -> Proxy s -> Bool # (>) :: Proxy s -> Proxy s -> Bool # (>=) :: Proxy s -> Proxy s -> Bool # max :: Proxy s -> Proxy s -> Proxy s # min :: Proxy s -> Proxy s -> Proxy s #
type Rep1 (Proxy :: k -> Type) | @since base-4.6.0.0
Instance details Defined in GHC.Internal.Generics type Rep1 (Proxy :: k -> Type) = D1 ('MetaData "Proxy" "GHC.Internal.Data.Proxy" "ghc-internal" 'False) (C1 ('MetaCons "Proxy" 'PrefixI 'False) (U1 :: k -> Type))
type Rep (Proxy t) | @since base-4.6.0.0
Instance details Defined in GHC.Internal.Generics type Rep (Proxy t) = D1 ('MetaData "Proxy" "GHC.Internal.Data.Proxy" "ghc-internal" 'False) (C1 ('MetaCons "Proxy" 'PrefixI 'False) (U1 :: Type -> Type))